Landon is writing a coordinate proof to show that the diagonals of a square are perpendicular to each other. she starts by assigning coordinates as given.

Answers:

Since GHJK is a square, the coordinates of H are (a,a)

The slope of KH is 1.

The slope of GJ is -1.

The product of the slopes of the diagonals is -1.

Therefore, KH is perpendicular ti GJ.

Solution:

1. Coodinates of H

xh=a, yh=a→Corrdinates of H=(xh, yh)=(a,a)

2. Slope of GJ

G=(0,a)=(xg,yg)→xg=0, yg=a

J=(a,0)=(xj,yj)→xj=a, yj=0

Slope of GJ=m=(yj-yg)/(xj-xg)

m=(0-a)/(a-0)

m=(-a)/(a)

m=-1

Slope of GJ is -1.

3. Product of the slopes of the diagonals

Slope of KH * Slope of GJ = (1)*(-1)

Slope of KH * Slope of GJ = -1

r and t.

both are 64 degrees.