Question

I need help with this! I'll mark Brainliest if it's correct.

Answer 1

Answers:
Coordinates of H are: (a,a)
The slope of segment GJ is: -1
The product of the slopes of the diagonals is: -1

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Explanation:

Point J has an x coordinate of x = a
Point G has a y coordinate of y = a
So point H has the coordinates (x,y) = (a,a)
We simply move straight up from point J to get to H. At the same time, we move horizontally across to go from G to H. This is why H has half the coordinates from each J and G

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As for the slope of GJ, we use the slope formula
m = (y2-y1)/(x2-x1)
m = (0-a)/(a-0)
m = -a/a
m = -1
So that shows why the slope of GJ is -1

Multiplying the slope of KH (1) and the slope of GJ (-1), we get
1 times -1 = -1
The product being -1 shows the diagonals KH and GJ are perpendicular. They form a 90 degree angle.