Question

Three vertices of parallelogram JKLM are J(1, 4), K(5, 3), and L(6,-3). Find the coordinates ofvertex M.The coordinates are MOD.

Answer 1

Given data:

The coordinate of first vertex is J(1, 4).

The coordinate of second vertex is K(5, 3).

The coordinate of third vertex is L(6,-3).

Assume the coordinate of M is (x, y).

The diagonal of the parallelogram intersect at the mid point, the mid point of the diagonal JL is,

$\begin{gathered} a=\frac{1+6}{2} \\ =\frac{7}{2} \\ b=\frac{4-3}{2} \\ =\frac{1}{2} \end{gathered}$

This is also the mid point of KM diagonal.

$\begin{gathered} \frac{7}{2}=\frac{x+5}{2} \\ x=2 \\ \frac{1}{2}=\frac{y+3}{2} \\ y=-2 \end{gathered}$

Thus, the coordinate of M is (2, -2).