Q2 of 29 Page 11

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)

Since, the coordinates of P, Q and R are 3, -5 and 6 respectively. We know that 6 > 3 > -5.

Therefore, d (P, Q) = d (Q, P) = 3 – (-5) = 3 + 5 = 8


d (Q, R) = d (R, Q) = 6 – (-5) = 6 + 5 = 11


and d (R, P) = d (P, R) = 6 – 3 = 3


i. Here, consider


d (P, Q) + d (Q, R) = 8 + 11 = 19 ≠ 3 = d (P, R)


So, this statement is false.


ii. Here, consider


d (P, R) + d (R, Q) = 3 + 11 = 14 ≠ 8 = d (P, Q)


So, this statement is false.


iii. Here, consider


d (R, P) + d (P, Q) = 3 + 8 = 11 = d (R, Q)


So, this statement is true.


iv. Here, consider


d (P, Q) – d (P, R) = 8 – 3 = 5 ≠ 11 = d (Q, R)


So, this statement is false.


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