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).