MCQ

True or False

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.

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

#### Options

True

False

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#### Solution

The co-ordinates of points P and Q are 3 and −5 respectively. We know that 3 > −5.

Now, d(P, Q) = 3 − (−5) = 3 + 5 = 8

The co-ordinates of points Q and R are −5 and 6 respectively. We know that 6 > −5.

Now, d(Q, R) = 6 − (−5) = 6 + 5 = 11

The co-ordinates of points P and R are 3 and 6 respectively. We know that 6 > 3.

Now, d(P, R) = 6 − 3 = 3

d(P,Q) - d(P,R) = 8 − 3 = 5; d(Q,R) = 11

So, d(P,Q) - d(P,R) ≠ d(Q,R)

Hence, the given statement is false.

Concept: Co-ordinates of Points and Distance

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