A parallelogram MNQR has vertices M(4, -6), N(10, 2), Q(8, 16) and R(x, y). Find…

A parallelogram MNQR has vertices M(4, -6), N(10, 2), Q(8, 16) and R(x, y). Find the coordinates of R.

Explanation

(overrightarrow{MN} = overrightarrow{RQ})

(begin{pmatrix} 4 – 10 \ – 6 – 2 end{pmatrix} = begin{pmatrix} x – 8 \ y – 16 end{pmatrix})

(implies 4 – 10 = x – 8)

(-6 = x – 8 implies x = -6 + 8 = 2)

(implies – 6 – 2 = y – 16)

(-8 = y – 16 implies y = -8 + 16 = 8)

The coordinate of R is (2, 8).