## 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

Lost your password? Please enter your email address. You will receive a link and will create a new password via email.

## Answers ( )

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 :Answer :S = (-5,0)T = (2,1)