The points A(5,-3), B(-2,4) and C(-1,7) are three vertices of a parallelogram ABCD. Find the coordinates of vertex D.

The points A(5,-3), B(-2,4) and C(-1,7) are three vertices of a parallelogram ABCD. Find the coordinates of vertex D.

$$\vec{D}=\vec{B} + (\vec{A}- \vec{B}) + (\vec{C}- \vec{B}) \\ \vec{D}=\not{ \vec{B} } + \vec{A} -\not{ \vec{B}} + (\vec{C}- \vec{B}) \\ \boxed{ \vec{D}=\vec{A} + (\vec{C}- \vec{B}) }\\\\ \vec{D}= \left( \begin{array}{c} 5\\-3\end{array} \right) + ( \left( \begin{array}{c} -1\\7\end{array} \right) - \left( \begin{array}{c} -2\\4\end{array} \right) )\\\\ \vec{D}= \left( \begin{array}{c} 5+(-1)-(-2)\\-3+7-4\end{array} \right)\\\\ \vec{D}= \left( \begin{array}{c} 5-1+2\\0\end{array} \right)\\\\ \vec{D}= \left( \begin{array}{c}6\\0\end{array} \right)\\\\$$

Notice that the point (-1, 7) is three units up and 1 unit to the right of point (-2, 4)

So, D will be three units up and one unit to the right of (5, -3)

So D is at (5 + 1, -3 + 3)  = (6, 0)

Here's a graph........https://www.desmos.com/calculator/2tucisvosv