Question

On a number line, co-ordinates of P, Q, R are 3,− 5 and 6 respectively. State with reason whether the following statement is true or false. d(P,R) + d(R,Q) = d(P,Q)  true false​

Answer 1

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.

Answer 2

Answer:

⭐Since, the coordinates of P, Q and R are 3, -5 and 6 respectively. We know that 6 > 3 > -5. So, this statement is false. So, this statement is false.⭐