1. If the distance between the points (2, –2) and (–1, x) is 5, one of the values of x is

(A) –2

(B) 2

(C) –1                                                 

(D) 1

Answer: (B)

Explanation: According to question

2. The mid-point of the line segment joining the points A (–2, 8) and B (– 6, – 4) is

(A) (– 4, – 6)                                       

(B) (2, 6)

(C) (– 4, 2)                                          

(D) (4, 2)

Answer:  (C)

Explanation: Let the coordinates of midpoint be (x, y) then

Therefore the coordinates are

3. The points A (9, 0), B (9, 6), C (–9, 6) and D (–9, 0) are the vertices of a

(A) Square                                          

(B) Rectangle

(C) Rhombus                                      

(D) Trapezium

Answer:  (B)

Explanation: Here we will calculate the measure of all four sides of the quadrilateral fromed by given points A, B, C and D.

Since, AB = CD and BC = AD

Therefore given points A,B,C and D are the vertices of a rectangle.

4. The distance of the point P (2, 3) from the x-axis is

(A) 2                                                               

(B) 3

(C) 1                                                               

(D) 5

Answer:  (B)

Explanation: Distance of the point P (2, 3) from the x-axis =Ordinate of the point (2, 3) i.e.3.

5. The distance between the points A (0, 6) and B (0, –2) is

(A) 6                                                   

(B) 8

(C) 4                                                   

(D) 2

Answer:  (B)

Explanation: Here, x₁ = 0, y₁ = 6, x₂ = 0, y₂ = –2

6. AOBC is a rectangle whose three vertices are vertices A (0, 3), O (0, 0) and B (5, 0). The length of its diagonal is

(A) 5                                                   

(B) 3

(C) √34                                               

(D) 4

Answer:  (C)

Explanation:

The length of the diagonal is distance between the points AB.

 The distance is calculated as,

7. If P (a/3, 4) is the mid-point of the line segment joining the points Q (– 6, 5) and R (– 2, 3), then the value of a is

(A) – 4                                                

(B) – 12

(C) 12                                                 

(D) – 6

Answer:  (B)

Explanation: As (a/3, 4) is the mid – point of the line segment joining the points Q (– 6, 5) and R (– 2, 3). Therefore

8. The coordinates of the point which is equidistant from the three vertices of the Δ AOB as shown in the figure is:

(A) (x, y)                                                         

(B) (y, x)

(C) (x/2, y/2)                                                  

(D) (y/2, x/2)  

Answer:  (A)

Explanation: As we have to find the coordinates which are equidistant from A and B, Let the points be (a, b).

Then (a, b) will be the midpoint of AB.

Therefore,

Hence the coordinates are (x, y)

9. A circle drawn with origin as the centre passes through The point which does not lie in the interior of the circle is

(C) (5, –1/2)                                       

(D) (–6, 5/2)

Answer:  (D)

Explanation:If the point lies in the interior of circle, the distance of the point from the centre should be less than radius of circle.

The radius of circle is the distance between origin and the point

Distance between origin and (-3/4, 1) is

Similarly the distance of points (2, 7/3) and (5, –1/2) is also less than 6.5

But the distance of (–6, 5/2) is equal to 6.5.

So the point (–6, 5/2) does not lie in the interior of circle.

10. If the distance between the points (4, p) and (1, 0) is 5, then the value of p is

(A) 4 only                                                        

(B) ± 4

(C) – 4 only                                                     

(D) 0

Answer:B

Explanation:   According to question:

11. The area of a triangle with vertices A (3, 0), B (7, 0) and C (8, 4) is:

(A) 14                                                 

(B) 28

(C) 8                                                   

(D) 6

Answer:  (C)

Explanation: Area of triangle is calculated as,

12. The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the

(A) I quadrant                                                 

(B) II quadrant

(C) III quadrant                                               

(D) IV quadrant

Answer: (D)

Explanation: Let the point be (x, y)

Then, by using section formula

Therefore, the point is (17/3, -8/3) which lies in fourth quadrant.

13. One of the two points of trisection of the line segment joining the points A (7, – 2) and B (1, – 5) which divides the line in the ratio 1:2 are:

(A) (5, –3)                                                       

(B) (5, 3)

(C) (–5, –3)                                                     

(D) (13, 0)

Answer:  (A)

Explanation: Required point of trisection that divides the given line in the ratio 1: 2 is

14. A line intersects the y-axis and x-axis at the points 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)

Answer:  (D)

Explanation: As the line intersects the y and x axis, let the coordinates be (0, b) and (a, 0) respectively. Since (2, –5) is the midpoint of the axis. Therefore,

Therefore, the coordinates are (0, –10) and (4, 0).

15. The ratio in which the point P (3/4, 5/12)divides the line segment joining the Points A (1/2, 3/2) and B (2, –5) is:

(A) 1:5                                                            

(B) 5:1

(C) 1:3                                                            

(D) 3:1

Answer:  (A)

Explanation: Let the ratio be m : n then, according to the question:

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