**Exercise 7.2›**

Choose the correct answer from the given four options:

Q1. The distance of the point P (2, 3) from the x-axis is

(A) 2 (B) 3 (C) 1 (D) 5

(A) 2 (B) 3 (C) 1 (D) 5

Solution 1

Q2. The distance between the points

A (0, 6) and B (0, –2) is (A) 6 (B) 8 (C) 4 (D) 2

A (0, 6) and B (0, –2) is (A) 6 (B) 8 (C) 4 (D) 2

Solution 2.

Q3. The distance of the point P (–6, 8) from the origin is

(A) 8 (B) 2 7 (C) 10 (D) 6

(A) 8 (B) 2 7 (C) 10 (D) 6

Solution 3.

Q4. The distance between the points (0, 5) and (–5, 0) is

(A) 5 (B) 5 2 (C) 2 5 (D) 10.

(A) 5 (B) 5 2 (C) 2 5 (D) 10.

Solution 4

Q5. 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

A (0, 3), O (0, 0) and B (5, 0). The length of its diagonal is (A) 5 (B) 3 (C) 34 (D) 4

Solution 1

Q6. The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is

(A) 5 (B) 12 (C) 11 (D) 7 5 +

(A) 5 (B) 12 (C) 11 (D) 7 5 +

Solution 2.

Q7. 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

(A) 14 (B) 28 (C) 8 (D) 6

Solution 2.

Q8. The points (–4, 0), (4, 0), (0, 3) are the vertices of a

(A) right triangle (B) isosceles triangle (C) equilateral triangle (D) scalene triangle

(A) right triangle (B) isosceles triangle (C) equilateral triangle (D) scalene triangle

Solution 2.

Q9. 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

(A) I quadrant (B) II quadrant (C) III quadrant (D) IV quadrant

Solution 2.

Q10. The point which lies on the perpendicular bisector of the line segment joining the points A (–2, –5) and B (2, 5) is

(A) (0, 0) (B) (0, 2) (C) (2, 0) (D) (–2, 0)

(A) (0, 0) (B) (0, 2) (C) (2, 0) (D) (–2, 0)

Solution 2.

Q11. The fourth vertex D of a parallelogram ABCD whose three vertices are A (–2, 3), B (6, 7) and C (8, 3) is

(A) (0, 1) (B) (0, –1) (C) (–1, 0) (D) (1, 0).

(A) (0, 1) (B) (0, –1) (C) (–1, 0) (D) (1, 0).

Solution 2.

Q12. If the point P (2, 1) lies on the line segment joining points A (4, 2) and B (8, 4), then

(A) AP = 1 3 AB (B) AP = PB (C) PB = 1 3 AB (D) AP = 1 2 AB.

(A) AP = 1 3 AB (B) AP = PB (C) PB = 1 3 AB (D) AP = 1 2 AB.

Solution 2.

Q13. If P , 4 3 a 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.

(A) – 4 (B) – 12 (C) 12 (D) – 6.

Solution 2.

Q14. The perpendicular bisector of the line segment joining the points A (1, 5) and B (4, 6) cuts the y-axis at

(A) (0, 13) (B) (0, –13) (C) (0, 12) (D) (13, 0) .

(A) (0, 13) (B) (0, –13) (C) (0, 12) (D) (13, 0) .

Solution 2.

Q15. The coordinates of the point which is equidistant from the three vertices of the ∆ AOB as shown in the Fig. 7.1 is (A) (x, y) (B) (y, x) (C) , 2 2 x y (D) , 2 2 y x .

Solution 2.

Q6. Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.

Solution 2.

Q6. Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.

Solution 2.

Q6. Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.

Solution 2.

Q6. Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.

Solution 2.

Q6. Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.

Solution 2.

Q7. There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?

Solution 3.

**‹Exercise 1.1 Exercise 1.3›**