You are given coordinates for two vertices of an isosceles right triangle. let's say the triangle is \(\delta abc\) and you're given the coordinates of \(a\) and \(b\), with \(\angle c\) as the right angle. how could you find the coordinates of \(c\) using the distance formula? support your answer with examples. there is more than one correct way to find the coordinates!

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough

check the picture below.