RD SHARMA SOLUTION CHAPTER-14 Coordinate Geometry| CLASS 10TH MATHEMATICS-EDUGROWN

Chapter 14 – Co-ordinate Geometry Exercise Ex. 14.1

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Chapter 14 – Co-ordinate Geometry Exercise Ex. 14.2

Question 1 (i)

Solution 1 (i)

Question 1 (ii)

Solution 1 (ii)

Question 1 (iii)

Solution 1 (iii)

Question 1 (iv)

Solution 1 (iv)

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Show that the points A(1,-2), B(3,6), C(5,10) and D(3,2) are the vertices of a parallelogram.Solution 7

Question 8

Prove that the points (1, 7), (4, 2), (-1, -1) and (-4, 4) are the vertices of a square.Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

The points A(2, 9), B(a, 5) and C(5, 5) are the vertices of triangle ABC right angled at B. Find the values of a and hence the area of ⧍ABC.Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Find a point which is equidistant from the points

A (-5, 4) and B (-1, 6). How many such points are there?Solution 21

Question 22

The centre of a circle is (2a, a – 7). Find the values of a if the circle passes through the point (11, -9) and has diameter units.Solution 22

Question 23

Ayush starts walking from his house to office, Instead of going to the office directly, he goes to bank first, from there to his daughter’s school and then reaches the office. What is the extra distance travelled by Ayush in reaching the office? (Assume that all distance covered are in straight lines). If the house is situated at (2, 4), bank at (5, 8) school at (13, 14) and office at (13, 26) and coordinates are in kilometer.Solution 23

Question 24

Solution 24

Question 25

If (-4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the (i) interior (ii) exterior of the triangle.Solution 25

Question 26

Solution 26

Question 27

Solution 27

Question 28

Solution 28

Question 29(i)

Show that the points A(5,6), B(1,5), C(2,1) and D(6,2) are the vertices of a square.Solution 29(i)

Question 29(ii)

Prove that the points A(2, 3), B(-2, 2), C(-1, -2), and D (3, -1) are the vertices of a square ABCD.Solution 29(ii)

Question 29(iii)

Solution 29(iii)

Question 30

Solution 30

Question 31

Solution 31

Question 32

Solution 32

Question 33

If the point P(x,y) is equidistant from the points A(5,1) and B(1,5), prove that x = y.Solution 33

Question 34

Solution 34

Question 35

Solution 35

Question 36

If the point P(k-1, 2) is equidistant from the points A(3, k) and B(k, 5), find the values of k.Solution 36

Question 37

If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), find p. Also, find the length of AB.Solution 37

Question 38

Solution 38

Question 39

Find the equation of the perpendicular bisector of the line segment joining points (7,1) and (3,5).Solution 39

Question 40

Prove that the points (3,0), (4,5), (-1,4) and (-2,-1), taken in order, form a rhombus. Also, find its area.Solution 40

Question 41

Solution 41

Question 42

Solution 42

Question 43

Solution 43

Question 44

If a point A(0,2) is equidistant from the points B(3,p) and C(p,5), then find the value of p.Solution 44

Question 45

Prove that the points (7, 10), (-2, 5) and (3, -4) are the vertices of an isosceles right triangle.Solution 45

Question 46

If the point P(x, 3) is equidistant from the points A(7, -1) and B(6, 8), find the value of x and the find the distance AP.Solution 46

Question 47

If A(3, y) is equidistant from the points P(8, – 3) and Q(7, 6), find the value of y and find the distance AQ.Solution 47

Question 48

If (0, -3) and (0, 3) are the two vertices of an equilateral triangle, find the coordinates of its third vertex.Solution 48

For an equilateral triangle, the perpendicular bisector of any side passes through the opposite vertex.

Both the points, (0, -3) and (0, 3), lie on the y-axis equidistant from the origin. Hence, the perpendicular bisector joining these two points is the x-axis.

Any point on the x-axis has the coordinates (a, 0).

The distance between (0, -3) and (0, 3) is 6.

Hence, the distance between (a, 0) and (0, 3) should also be 6.

6² = (a – 0)² + (0 – 3)²

36 = a² + 9

a² = 27

Question 49

If the point P(2, 2) is equidistant from the points A(-2, k) and B(-2k, -3), find k. Also, find the length of AP.Solution 49

Question 50

Show that ∆ABC, where A (-2, 0), B (2, 0) C (0, 2) and ∆PQR, where P (-4, 0), Q (4, 0), R (0, 4) are similar.Solution 50

Using the distance formula,

AB=

AC=

BC=

PQ=

PR=

QR=

Now,

ΔABC ~ ΔPQR

by the SSS test.Question 51

Solution 51

Question 52

Find the circumcentre of the triangle whose vertices are (-2,-3), (-1,0), (7,-6).Solution 52

Question 53

Solution 53

Question 54

Find the centre of the circle passing through (5, -8), (2, -9) and (2, 1).Solution 54

Question 55

Solution 55

Question 56

Solution 56

Question 57

Solution 57

Chapter 14 – Co-ordinate Geometry Exercise Ex. 14.3

Question 1

Solution 1

Question 2

Find the points of trisection of the line segment joining the points:

(i) (5, -6) and (-7, 5), (ii) (3, -2) and (-3,-4), (iii) (2,-2) and (-7,4).Solution 2

(i)



(ii)



(iii)

Question 3

Solution 3

Question 4

Solution 4

Question 5

If P(9a – 2, -b) divides the line segment joining A(3a + 1, -3) and B(8a, 5) in the ratio 3 : 1, find the values of a and b.Solution 5

Question 6

If (a, b) is the mid-point of the line segment joining the points A (10, -6), B(k, 4) and a – 2b = 18, find the value of k and the distance AB.Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

If the points P,Q(x, 7), R, S(6, y) in this order divide the line segment joining A(2, p) and B (7, 10) in 5 equal parts, find x, y and p.Solution 9

Question 10

Solution 10

Question 11(i)

Solution 11(i)

Question 11(ii)

Solution 11(ii)

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

  *Note: (i) Answer given in the book is incorrect.Question 15

Solution 15

Question 16

Prove that (4,3), (6,4), (5,6) and (3,5) are the angular points of a square.Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Find the ratio in which the line segment joining the points A (3, -3) and B (-2, 7) is divided by x- axis. Also, find the coordinates of the point of division.Solution 19

Let the point on the x-axis be (a, 0).

Let this point divide the line segment AB in the ratio of r : 1.

Using the section formula for the y-coordinate, we get

Question 20

Find the ratio in which the point P(x, 2) divides the line segment joining the points A (12, 5) and B (4, -3). Also, find the value of x.Solution 20

Question 21

Find the ratio in which the point P(-1, y) lying on the line segment joining A(-3, 10) and B(6, -8) divides it. Also find the value of y.Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

In what ratio does the point (-4,6) divide the line segment joining the points A(-6,10) and B(3,-8)?Solution 25

Question 26

Solution 26

Question 27

Solution 27

Question 28

Solution 28

Question 29

Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, -3). Hence, find m.Solution 29

Let P divides the line segment AB is the ratio k: 1.

So, the ratio is 1:1.

Also, 

Question 30

Solution 30

Question 31

Solution 31

Question 32

Solution 32

Question 33

Solution 33

Question 34

Show that the points A(1,0) B(5,3), C(2,7) and D(-2,4) are the vertices of a parallelogram.Solution 34

Question 35

Solution 35

Question 36

Solution 36

Question 37

Solution 37

Question 38

Points P, Q, R and S divide the line segment joining the points A(1, 2) and B(6, 7) in 5 equal parts. Find the coordinates of the points P, Q, and R.Solution 38

The difference between the x-coordinates of A and B is 6 – 1 = 5

Similarly, the difference between the y-coordinates of A and B is 7 – 2 = 5

Hence, if the line segment joining A(1, 2) and B(6, 7) is divided into 5 equal parts by the points P, Q, R and S, then the coordinates of P, Q, R and S can be found out by increasing the x and the y coordinates of A by 1 successively.

Hence, the coordinates of P are (1 + 1, 2 + 1) = (2, 3)

The coordinates of Q are (2 + 1, 3 + 1) = (3, 4)

The coordinates of R are (3 + 1, 4 + 1) = (4, 5)Question 39

Solution 39

Question 40

Solution 40

Question 41

Solution 41

Question 42

Solution 42

Question 43

Solution 43

Question 44

Solution 44

Question 45

Solution 45

Question 46

If two vertices of a parallelogram are (3,2), (-1,0) and the diagonals cut at (2,-5), find the other vertices of the parallelogram.Solution 46

Question 47

If the coordinates of the mid-points of the sides of a triangle are (3,4), (4,6), and (5,7), find its vertices.Solution 47

Question 48

Solution 48

Question 49

Solution 49

Question 50 (i)

Solution 50 (i)

Question 50 (ii)

Points A(3, 1), B(5, 1), C(a, b) and D(4, 3) are vertices of a parallelogram ABCD. Find the values of a and b.Solution 50 (ii)

Given: ABCD is a parallelogram

We know that, diagonals of a parallelogram bisect each other.

Therefore, midpoints of diagonals coincide

The midpoints of AC and BD coincide.

Question 51

Solution 51

Question 52 (i)

Points P and Q trisect the line segment joining the points A(-2, 0) and B(0, 8) such that P is near to A. Find the coordinates of P and Q.Solution 52 (i)

As P and Q trisect AB and P is near to A.

Therefore, P divides AB in the ratio 1:2.

Also, Q divides AB in the ration 2:1.

Question 52 (ii)

Solution 52 (ii)

Question 53

Solution 53

Question 54

Solution 54

Question 55

Solution 55

Question 56

A point P divides the line segment joining the points A(3,-5) and B(-4,8), such that  . If P lies on the line x + y = 0, then find the value of k.Solution 56

Given points are A(3,-5) and B(-4,8).

P divides AB in the ratio k : 1.

Using the section formula, we have:

Coordinate of point P are {(-4k+3/k+1)(8k-5/k+1)}

Now it is given, that P lies on the line x+y = 0

Therefore,

-4k+3/k+1 + 8k-5/k+1 =0

=> -4k+3+8k-5 =0

=> 4k -2 =0

=> k=2/4

=> k=1/2

Thus, the value of k is 1/2.Question 57

The mid – point P of the line segment joining the points A (-10, 4) and B (-2, 0) lies on the line segment joining the points C (-9, -4) and D (-4, y). Find the ratio in which P divides CD. Also, find the value of y.Solution 57

Question 58

If the point C(-1, 2) divides internally the line segment joining the points A(2, 5) and B(x, y) in the ratio 3 : 4, find the value of x² + y².Solution 58

Question 59

ABCD is a parallelogram with vertices A(x₁, y₁), B(x₂, y₂) and C (x₃, y₃). Find the coordinates of the fourth vertex D in terms of x₁, x₂, x₃, y₁, y₂ and y₃.Solution 59

Question 60

The points A (x₁, y₁), B(x₂, y₂) and C (x₃, y₃) are the vertices of ⧍ABC.

 i. The median from A meets BC at D. Find the coordinates of the point D.

 ii. Find the coordinates of the point P on AD such that AP : PD = 2 : 1.

 iii. Find the points of coordinates Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1.

 iv. What are the coordinates of the centroid of the triangle ABCSolution 60

Chapter 14 – Co-ordinate Geometry Exercise Ex. 14.4

Question 1(i)

Solution 1(i)

Question 1(ii)

Solution 1(ii)

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Prove analytically that the line segment joining the middle points of two sides of a triangle is equal to half of the third side.Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Chapter 14 – Co-ordinate Geometry Exercise Ex. 14.5

Question 1

Solution 1

Question 1 (iv)

Find the area of a triangle whose vertices are

(1, -1), (-4, 6) and (-3, -5)Solution 1 (iv)

Area of triangle with vertices (x₁, y₁), (x₂, y₂) and (x₃, y₃) is

Therefore, area of triangle with given vertices is

Hence, the area of triangle will be 24 sq. units.Question 1 (v)

Find the area of a triangle whose vertices are

(-5, 7), (-4, -5) and (4, 5)Solution 1 (v)

Area of triangle with vertices (x₁, y₁), (x₂, y₂) and (x₃, y₃) is

Therefore, area of triangle with given vertices is

Hence, the area of triangle will be 53 sq. units.Question 2(i)

Solution 2(i)

Question 2(ii)

Solution 2(ii)

Question 2(iii)

Find the area of the quadrilaterals, the coordinates of whose vertices are

(-4,-2), (-3,-5), (3,-2), (2,3)Solution 2(iii)

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Find the area of a quadrilateral ABCD, the coordinates of whose vertices are A(-3, 2), B(5, 4), C(7, -6) and D(-5, -4).Solution 6

Question 7

In ⧍ABC, the coordinates of vertex A are (0, -1) and D(1, 0) and E(0, 1) respectively the mid-points of the sides AB and AC. If F is the mid-point of side BC, find the area of ⧍DEF.Solution 7

Question 8

Find the area of the triangle PQR with Q (3, 2) and the mid-points of the sides through Q being (2, -1) and (1, 2).Solution 8

Question 9

If P(-5, -3), Q(-4, -6), R(2, -3) and S(1, 2) are the vertices of a quadrilateral PQRS, find its area.Solution 9

Question 10

If A (-3, 5), B(-2, -7), C(1, -8) and D(6, 3) are the vertices of a quadrilateral ABCD, find its area.Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13 (i)

If the vertices of a triangle are (1,-3), (4,p) and (-9, 7) and its area is 15 sq. units, find the value (s) of p.Solution 13 (i)

Question 13 (ii)

Find the value of k so that the area of triangle ABC with A(k + 1, 1), B(4, -3) and C(7, -k) is 6 square units.Solution 13 (ii)

Area of triangle with vertices (x₁, y₁), (x₂, y₂) and (x₃, y₃) is

Hence, the value of k is 3.Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Find the value of a for which the area of the triangle formed by the points A(a, 2a), B(-2, 6) and C (3, 1) is 10 sequare units.Solution 20

Question 21

If a ≠ b ≠ 0, prove that the points (a, a²), (b, b²), (0, 0) are never collinear.Solution 21

Let the points (a, a²), (b, b²), (0, 0) represent a triangle. If we can prove that the area of the triangle so formed is not equal to zero, then we can prove that the points (a, a²), (b, b²), (0, 0) are never collinear.

Area of a triangle is given by

Now b≠a≠0.

So,

b – a≠0,

Δ≠0

Thus, points (a, a²), (b, b²), (0, 0) are never collinear.Question 22

The area of a triangle is 5 sq. units. Two of its vertices are at (2, 1) and (3, -2). If the third vertex is (7/2, y), find y.Solution 22

Area of a triangle is given by Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26

Question 27

Solution 27

Question 28

Solution 28

Question 29

Solution 29

Question 30

Find the value (s) of k for which the points (3k – 1, k – 2), (k, k – 7) and (k – 1, -k – 2) are collinear.Solution 30

Let the points be A, B and C respectively.

If A, B and C are collinear, then the area of ∆ABC is zero.

Question 31

If the points A(-1, -4), B(b, c) and C(5, -1) are collinear and 2b + c = 4, find the values of b and c.Solution 31

Question 32

If the points A(-2, 1), B(a, b) and C(4, -1) are collinear and a – b = 1, find the values of a and b.Solution 32

Question 33

If the points A(1, -2), B(2, 3), C(a, 2) and D(-4, -3) form a parallelogram, find the value of a and height of the parallelogram taking AB as base.Solution 33

Question 34

A(6, 1), B(8, 2) and C(9, 4) are three vertices of a parallelogram ABCD. If E is the mid-point of DC, find the area of ⧍ADE.Solution 34

Question 35

If D(-1/5, 5/2), E(7, 3) and F(7/2, 7/2) are the mid-points of sides of ⧍ABC, find the area of ⧍ABCSolution 35

Chapter 14 – Co-ordinate Geometry Exercise 14.63

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

A line Segement is of length 10 units. If the coordinates of its one end are (2,3) and the abscissa of the other end is 10, then its ordinate is

(a) 9,6

(b) 3,-9

(c) -3,9

(d) 9,-6Solution 6

Question 7

Solution 7

So, the correct option is (d).Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Chapter 14 – Co-ordinate Geometry Exercise 14.64

Question 11

Solution 11

Question 12

If (-1,2),(2,-1) and (3,1) are any three vertices of a parallelogram, then

(a) a = 2, b = 0

(b) a = -2, b = 0

(c) a = -2, b = 6

(d) a = 6, b = 2Solution 12

Note: The answer does not match the options.Question 13

If A (5,3), B(11,-5) and P(12,y) are the vertices of a right triangle right angled at P, then y = 

(a) – 2,4

(b) -2 ,4

(c) 2, -4

(d) 2,4Solution 13

Question 14

The area of the triangle formed by (a,b+c), (b,c+a) and (c,a+b) is 

(a)  a+b+c

(b) abc

(c) (a+b+c)²

(d) 0Solution 14

Question 15

If (x,2),(-3,-4) and (7,-5) are collinear, then x = 

(a) 60

(b) 63

(c) -63

(d) -60Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

The line segment joining points (-3,4), and (1,-2) is divided by y – axis in the ratio

(a) 1 : 3

(b) 2 : 3

(c) 3 : 1

(d) 2: 3Solution 20

Question 21

The ratio in which (4,5) divides the join of (2,3) and (7,8) is 

(a) -2 : 3

(b) -3 : 2 

(c) 3 : 2

(d) 2 : 3Solution 21

Question 22

The ratio in which the x-axis divides the segment joining (3,6) and (12,-3) is

(a) 2:1

(b) 1 :2

(c) -2 : 1

(d) 1 : -2 Solution 22

Question 23

If the centrroid  of the triangle formed by the points (a,b),(b,c) and (c,a) is at the origin, then a³ + b³ + c³ = 

(a) abc

(b) 0

(c) a+b+c

(d) 3abcSolution 23

Question 25

If the centroid of the triangle formed by (7, x), (y, -6) and (9, 10) is at (6, 3), then (x, y) =

(a) (4, 5)

(b) (5, 4)

(c) (-5, -2)

(d) (5, 2)Solution 25

Question 24

If points A(3, 1), B(5, p) and C(7, -5) are collinear, then p =

(a) -2

(b) 2

(c) -1

(d) 1Solution 24

As the points A, B and C are collinear, then the area formed by these three points is 0.

Area of triangle with vertices (x₁, y₁), (x₂, y₂) and (x₃, y₃) is

Hence, the value of p is -2.

Chapter 14 – Co-ordinate Geometry Exercise 14.65

Question 26

The distance of the point (4, 7) from the x-axis is

(a) 4

(b) 7

(c) 11

(d) Solution 26

We know, distance of point (x, y) from x-axis is y.

Hence, distance of point (4, 7) from x-axis is 7.

Hence, correct option is (b).Question 27

The distance of the point (4, 7) from the y-axis is

(a) 4

(b) 7

(c) 11

(d) Solution 27

We know distance of point (x, y) from y-axis is x.

Hence distance of point (4, 7) from y-axis is 4.

Hence, correct option is (a).Question 28

If P is a point on x-axis such that its distance from the origin is 3 units, then the coordinates of a point Q on OY such that OP = OQ, are

(a) (0, 3)

(b) (3, 0)

(c) (0, 0)

(d) (0, -3)Solution 28

Given P is a point on x-axis

Hence P = (x, 0)

Distance from the origin is 3

Hence P = (3, 0)

Given Q is a point on y-axis

So Q is (0, y)

Given that OP = OQ

implies OQ = 3

Distance of Q from the origin is 3

Hence y = 3

implies Q = (0, 3)

Hence, correct option is (a).Question 29

If the point (x, 4) lies on a circle whose centre is at the origin and radius is 5, then x =

(a) ±5

(b) ±3

(c) 0

(d) ±4Solution 29

Question 30

If the point P (x, y) is equidistant from A(5, 1) and B (-1, 5), then

(a) 5x = y

(b) x = 5y

(c) 3x = 2y

(d) 2x = 3ySolution 30

Question 31

If points A (5, p), B (1, 5), C (2, 1) and D (6, 2) form a square ABCD, then p =

(a) 7

(b) 3

(c) 6

(d) 8Solution 31

Question 32

Solution 32

Question 33

The coordinates of a point on x-axis which lies on the perpendicular bisector of the line segment joining the points (7, 6) and (-3, 4) are

(a) (0, 2)

(b) (3, 0)

(c) (0, 3)

(d) (2, 0)Solution 33

Question 34

If the centroid of the triangle formed by the points (3, -5), (-7, 4), (10, -k) is at the point (k, – 1), then k =

(a) 3

(b) 1

(c) 2

(d) 4Solution 34

Question 35

If (-2, 1) is the Centroid of the triangle having its vertices at (x, 2), (10, -2), (-8, y), then x, y satisfy the relation

a. 3x + 8y = 0

b. 3x – 8y = 0

c. 8x + 3y = 0

d. 8x = 3ySolution 35

The Centroid of the triangle is given by

x=-8 and y=3 satisfy(a) 3x + 8y = 0.Question 36

The coordinates of the fourth vertex of the rectangle formed by the points (0, 0), (2, 0), (0, 3) are

(a) (3, 0)

(b) (0, 2)

(c) (2, 3)

(d) (3, 2)Solution 36

Question 37

The length of a line segment joining A(2, -3) and B is 10 units. If the abscissa of B is 10 units, then its ordinates can be

(a) 3 or -9

(b) -3 or 9

(c) 6 or 27

(d) -6 or -27Solution 37

Question 38

The ratio in which the line segment joining P(x₁, y₁) and Q(x₂, y₂) is divided by x-axis is

(a) y₁ : y₂

(b) -y₁ : y₂

(c) x₁ : x₂

(d) -x₁ : x₂Solution 38

Question 39

The ratio in which the line segment joining points A(a₁, b₁) and B(a₂, b₂) is divided by y-axis is

(a) -a₁ : a₂

(b) a₁ : a₂

(c) b₁ : b₂

(d) -b₁ : b₂Solution 39

Chapter 6 – Co-ordinate Geometry Exercise 6.66

Question 40

Solution 40

Question 41

If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (-2, 5), then the coordinates of the other end of the diameter are

(a) (-6, 7)

(b) (6, -7)

(c) (6, 7)

(d) -6, -7)Solution 41

Question 42

The coordinates of the point P dividing the line segment joining the points A (1, 3) and B (4, 6) in the ratio 2 : 1 are

(a) (2, 4)

(b) (3, 5)

(c) (4, 2)

(d) (5, 3)Solution 42

Question 43

In the figure, the area of ΔABC (in square units) is

(a) 15

(b) 10

(c) 7.5

(d) 2.5Solution 43

Question 44

The point on the x-axis which is equidistant from points (-1, 0) and (5, 0) is

(a) (0, 2)

(b) (2, 0)

(c) (3, 0)

(d) (0, 3)Solution 44

Question 45

Solution 45

Question 46

If P(2, 4), Q(0,3), R (3, 6) and S (5, y) are the vertices of a parallelogram PQRS, then the value of y is

(a) 7

(b) 5

(c) -7

(d) -8Solution 46

Question 47

If A(x, 2), B (-3, -4) and C (7, -5) are collinear, then the value of x is

(a) -63

(b) 63

(c) 60

(d) -60Solution 47

Question 48

Solution 48

Chapter 14 – Co-ordinate Geometry Exercise 14.67

Question 49

If the point P(2, 1) lies on the line segment joining points A (4, 2) and B (8, 4), then

Solution 49

Question 50

A line intersects the y-axis and x-axis at P and Q, respectively, If (2, -5) is the mid-point of PQ, then the coordinates of P and Q are respectively

a. (0, -5) and (2, 0)

b. (0, 10) and (-4, 0)

c. (0, 4) and (-10, 0)

d. (0, -10) and (4, 0)Solution 50

Question 51

If the point (k, 0) divides the line segment joining the points A(2, -2) and B(-7, 4) in the ratio 1 : 2, then the value of k is

(a) 1

(b) 2

(c) -2

(d) -1Solution 51

As the point (k, 0) divides the line segment AB in the 1:2

Hence, option (d) is correct.