SOLUTION: I'm so lost on this question! Please help!! " use coordinate geometery to prove that the diagonals of a square are perpendicular"

Question 397109: I'm so lost on this question! Please help!!
" use coordinate geometery to prove that the diagonals of a square are perpendicular"
Found 2 solutions by robertb, solver91311:
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let A(0,0), B(a,0), C(0,a), and D(a,a) be the vertices of the square.
Then line AD has slope , while
line BC has slope .
Hence the slopes are negative reciprocals of each other, and the lines AD and BC are perpendicular.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Since you can translate or rotate axes any way you like, there is no loss of generality if you place your square so that one vertex is at the origin, one side coincident with the y-axis and one side coincident with the x-axis.

Let represent the measure of a side of the square. Then and are the coordinates of the 4 vertices.

One diagonal is contained in the line that passes through and . The slope of this line, call it is given by the slope formula:

The other diagonal is contained in the line that passes through and . The slope of this line, call it is given by the slope formula:

But then

Therefore the diagonals are perpendicular because:

John

My calculator said it, I believe it, that settles it

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