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Question

# If the three consecutive vertices of a parallelogram PQRS are P(–9, 1), Q(–15, –1) and R(15, –1), then the coordinates of S are

A
(-9, 21)
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B
(-21, -1)
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C
(21, 1)
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D
(1, 21)
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Solution

## The correct option is C (21, 1)Given that the three consecutive vertices of the parallelogram are P(–9, 1), Q(–15, –1) and R(15, –1). Let the coordinates of the fourth vertex S be (a, b). We know that the diagonals of a parallelogram bisect each other. Therefore, O is the mid-point of PR as well as QS. Now, mid-point of PR =(15−92,−1+12)=(3,0) Mid-point of QS =(−15+a2,−1+b2) ∴ −15+a2=3 and −1+b2=0 ⇒ −15+a=6 and −1+b=0 ⇒a=6+15=21 and b=1 Thus, the coordinates of fourth vertex S are (21, 1). Hence, the correct answer is option (c).

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