Q 1) Do as directed : [10] (i) If P-Q-R and d(P,Q)=3, d(P,R)= 16, then find d(Q,R). (ii) Point P is the midpoint of seg AB. If AB=9, then find l(PB). (iii) Co-ordinates of P and Q are -2 and -5 respectively. Find d (P,Q).
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Step-by-step explanation:
(i) P-Q-R
d(P,R) = d(P,Q) + d(Q,R)
16 = 3 + d(Q,R)
16 – 3 = d(Q,R)
d(Q,R) = 13.
(ii) A midpoint divides the segment into two equal parts.
Therefore, AP = PB ------(i)
l(AB) = l(AP) + l(PB)
9 = 2 l(PB)------(from i)
l(PB) = 9 ÷ 2
therefore l(PB) = 4.5.
(iii) Co-ordinate of P = -2
Co-ordinate of Q = -5
d(P,Q) = -2 - (-5)
= -2 + 5
= 3.
d(P,Q) = 3.
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