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

Options

• True

• False

Answer 1

This statement is False.

Explanation:

The co-ordinates of points P, Q and R is 3, −5 and 6 respectively.

We know that 3 > −5

∴ d(P, Q) = 3 − (−5)

∴ d(P, Q) = 3 + 5 

∴ d(P, Q) = 8

We know that 6 > −5

∴ d(Q, R) = 6 − (−5)

∴ d(Q, R) = 6 + 5

∴ d(Q, R) = 11

We know that 6 > 3

∴ d(P, R) = 6 − 3

∴ d(P, R) = 3

∴ d(P, Q) + d(Q, R)

= 8 + 11

= 19

But d(P, R) = 3

So, d(P, Q) + d(Q, R) ≠ d(P, R)