## The diagonals of a quadrilateral QRST intersect at P(-1,3). QRST has vertices at Q(3,6) and R(-4,5). What must be the coordinates of S and T

Question

The diagonals of a quadrilateral QRST intersect at P(-1,3). QRST has vertices at Q(3,6) and R(-4,5). What must be the coordinates of S and T to ensure that QRST is a parallelogram

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3 weeks 2021-09-08T06:10:52+00:00 1 Answer 0

1. S = (-5,0)

T = (2,1)

Step-by-step explanation:

Step 1 :

Given

Q = (3,6) and R = (-4,5). P = (-1,3)

Let S be (a,b) and T be (c,d)

The diagonals of a parallelogram bisect each other. so in order to ensure that QRST is a parallelogram, P must be the mid point of the diagonals QS and RT.

Step 2 :

P is the midpoint  of QS

So we have (3+a) ÷ 2 =  -1  and (6 + b) ÷ 2 = 3

=> 3 + a = -2    and 6 + b = 6

=> a = -5  and b =0

So S should be (-5,0)

Step 3 :

P is the midpoint  of RT

So we have (-4+c) ÷ 2 =  -1  and (5 + d) ÷ 2 = 3

=> -4+ c = -2    and 5 + d = 6

=> c = 2  and d =1

So T should be (2,1)

Step 4 :