Question

The vertices of a square are A(–2, 4), B(4, 4), C(4, –2), and D(–2, –2). The diagonals of the square intersect at their midpoints.

What are the coordinates of the midpoint where the diagonals intersect?

(1, 1)
(–1, 4)
(2, 2)
(–3, 3)

Answer 1

A(–2, 4), B(4, 4), C(4, –2), D(–2, –2)
-> select some diagonal: AC
midpoint is at A+(1/2)*AC

-> calculate vector AC:
AC=(4-(-2),-2-4)=(6,-6)
-> calculate half length of AC:
(1/2)*AC=(3,-3)

A+(1/2)*AC=
(-2,4)+(3,-3)=(1,1) which is the midpoint

so the first option is correct