Question

Determine the coordinates of the intersection of the diagonals of square ABCD with verticals A(-4,6), B(5,6) C(4,-2), and D(-5,-2)

Answer 1

Given:

Vertices of a square are A(-4,6), B(5,6) C(4,-2), and D(-5,-2).

To find:

The intersection of the diagonals of square ABCD.

Solution:

We know that diagonals of a square always bisect each other. It means intersection of the diagonals of square is the midpoint of diagonals.

In the square ABCD, AC and BD are two diagonals. So, intersection of the diagonals is the midpoint of both AC and BD.

We can find midpoint of either AC or BD because both will result the same.

Midpoint of A(-4,6) and C(4,-2) is

$Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

$Midpoint=\left(\dfrac{-4+4}{2},\dfrac{6+(-2)}{2}\right)$

$Midpoint=\left(\dfrac{0}{2},\dfrac{6-2}{2}\right)$

$Midpoint=\left(\dfrac{0}{2},\dfrac{4}{2}\right)$

$Midpoint=\left(0,2\right)$

Therefore, the intersection of the diagonals of square ABCD is (0,2).