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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.

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 class=

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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

fichoh

Using the square GHJK given, the coordinate assignment and the slopes of the lines can be deduced thus:

1.)

The coordinates of H are the y-coordinate of G and the x-coordinate of H. Hence, H(a, a)

2.)

The perpendicular line with a positive slope is the line KH with a slope of 1.

3.)

The perpendicular line GJ has a negative slope, hence, the slope of GJ is - 1

4.)

The product of the slopes : GJ × KH = - 1 × 1 = - 1

Learn more : brainly.com/question/10613585

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