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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
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Solution
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)
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