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

S (1 , 0)

T (7 , 1)

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)