Geometry question....

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

write the slope intercept form equation for both diagonals:

AC and BD

AC:
m = (- 2 -6) / (4+4) = -1

(y - 6)/(x + 4) = -1

y = -x + 2

BD:
m = (-2-6) / (-5 - 5) = 4/5
(y + 2) / (x + 5) = 4/5
y = 4/5x + 2

equal both equation:
-x + 2 = 4/5 x + 2
x = 0
y = 2

(0, 2) intersection of diagonals

Find equations of AC and BD which are the diagonals of ABCD using y = mx + b for each line. Then solve the system of equations.

AC

y = mx + b

m = (6 --2)/(- 4 - 4) = 8/- 8 = - 1

y = - x + b

6 = - - 4+ b

6 = 4 + b

2 = b

y = - x + 2

BD

y = mx + b

m = (6 -- 2)/(5 --5) = 8/10 = 4/5

y = 4/5x + b

- 2 = 4/5(- 5) + b

- 2 = - 4 + b

2 = b

y = 4/5x + 2

system is

y = - x + 2
y = 4/5x + 2

subtract equations

0 = - 9/5x

0 = x

substitute 0 for x in one of the original equations and solve for y. Let's choose equation 1 and we get

y = - x + 2

y = 0 + 2

y = 2

so (0,2)

so easiest would be to see if midpoints were the same.(x+x/2, y+y/2)
midpt of AC (0,2) and BD (0, 2) so this is where they intersect.
if this didn't work you would of had to write the equation of the lines then use a system of equations to solve for intersection.