Question

Find the coordinates of the intersection of the diagonals of parallelogram QRST with verticesQ(-8, 1), R(2, 1), S(4,-3), and T(-6,-3).The coordinates of the intersection are

Answer 1

Lets draw the parallelogram:

Since diagonals QS and RT divide each other into segments of equal lenght, the diagonal bisect each other.

This means that the intersection point A is the middle point of segment QS (or TR). Therefore, we need to compute the middle point of one of segment.

The middle point formula is

$A=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

where

$\begin{gathered} T=(x_1,y_1)=(-6,-3) \\ R=(x_2,y_2)=(2,1) \end{gathered}$

By substituting these values into the middle point formula ,we get

$A=(\frac{-6+2}{2},\frac{-3+1}{2})$

which gives

$\begin{gathered} A=(\frac{-4}{2},\frac{-2}{2}) \\ A=(-2,-1) \end{gathered}$

Therefore, the coordinates of the intersection points are (-2, -1).