Question

The diagonals of a quadrilateral QRST intersect at P(2,3). QRST has vertices at Q(3,6) and R(-3,5). What must be the coordinates of S and T to ensure that QRST is a parallelogram?

Answer 1

Answer:

S (1 , 0)

T (7 , 1)

Step-by-step explanation:

If QRST is a parallelogram, P is the mid point of segment QS and segment RT.

Basic formula for mid-point of segment: ((x1+x2)/2 , (y1+y2)/2)

T (x₁ , y₁)    S (x₂ , y₂)   P (2 , 3)    Q (3 , 6)   R (-3 , 5)

2 = (x₁ + (-3))/2         x₁ = 7

3 = (y₁ + 5)/2            y₁ = 1

T (7 , 1)

2 = (x₂ + 3))/2         x₂ = 1

3 = (y₂ + 6)/2           y₂ = 0

S (1 , 0)