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 Hxh=a, yh=a→Corrdinates of H=(xh, yh)=(a,a)2. Slope of GJG=(0,a)=(xg,yg)→xg=0, yg=aJ=(a,0)=(xj,yj)→xj=a, yj=0Slope of GJ=m=(yj-yg)/(xj-xg)m=(0-a)/(a-0)m=(-a)/(a)m=-1Slope of GJ is -1.3. Product of the slopes of the diagonalsSlope of KH * Slope of GJ = (1)*(-1)Slope of KH * Slope of GJ = -1