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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 =(1592,1+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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