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(R,P) + D(P,Q) = D(R,Q) - Geometry

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

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(R,P) + d(P,Q) = d(P, R) + d(P,Q) = 3 + 8 = 11; d(R,Q) = d(Q, R) = 11
So, d(R,P) + d(P,Q) = d(R,Q)
Hence, the given statement is true.

Concept: Co-ordinates of Points and Distance

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Chapter 1 Basic Concepts in Geometry
Problem set 1 | Q 2.3 | Page 11