Question 717966: Find 4 values for k so that (-1,2), (-10,5) and (-4,k) are the vertices of a right triangle.
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! Starting with Distance Formula, First take the square of distance between each point.
One variable assigning form can give like this:
D[1] (-1,2) to (-10,5), 
D[2] (-1,2) to (-4,k), 
D[3] (-10,5) to (-4,k), 
Three equations using pythagorean theorem can be written for those distance squared expressions:
 ,
and
 ,
and
Take the expressions for each and fill into the pythagorean theorem equations, and solve for k. I did not finish the solution beyond what I wrote and posted so far.
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