Q4 of 29 Page 11

Co-ordinate of point P on a number line is - 7. Find the co-ordinates of points on the number line which are at a distance of 8 units from point P.

Let the point 8 units away from P be Q, then d (P, Q) = 8 where the coordinate of P is -7.

So, we have either of the following two cases:


Case I- If P > Q, then


d (P, Q) = P – Q


⇒ 8 = - 7 – Q ⇒ Q = - 7 – 8 = - 15


Case II- If P < Q, then


d (P, Q) = Q – P


⇒ 8 = Q – (-7) ⇒ Q = 8 + (-7) = 8 – 7 = 1


Hence, the coordinates of the required points are -15 and 1.


More from this chapter

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2

On a number line, co-ordinates of P, Q, R are 3, - 5 and 6 respectively. State with reason whether the following statements are true or false.

i. d(P,Q) + d(Q,R) = d(P,R)


ii. d(P,R) + d(R,Q) = d(P,Q)


iii. d(R,P) + d(P,Q) = d(R,Q)


iv. d(P,Q) - d(P,R) = d(Q,R)

 3

Co-ordinates of some pairs of points are given below. Hence find the distance between each pair.

i. 3, 6 ii. - 9, - 1


iii. - 4, 5 iv. x, - 2


v. x + 3, x – 3 vi. -25, - 47


vii. 80, - 85

 5

Answer the following questions.

i. If A - B - C and d(A,C) = 17, d(B,C) = 6.5 then d (A,B) = ?


ii. If P - Q - R and d(P,Q) = 3.4, d(Q,R)= 5.7 then d(P,R) = ?

 6

Co-ordinate of point A on a number line is 1. What are the co-ordinates of points on the number line which are at a distance of 7 units from A?