SOLUTION: Acute isosceles triangle ABC has vertices A(-2,-1), B(3,13), with point C on the line x=-7. If AB=BC, then find the coordinates of C.

Algebra ->  Graphs -> SOLUTION: Acute isosceles triangle ABC has vertices A(-2,-1), B(3,13), with point C on the line x=-7. If AB=BC, then find the coordinates of C.      Log On


   



Question 1100224: Acute isosceles triangle ABC has vertices A(-2,-1), B(3,13), with point C on the line x=-7. If AB=BC, then find the coordinates of C.
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!

If AB=BC, then (AB)^2 = (AC)^2; so we can solve the equation that says the squares of the distances are equal.

Using the distance formula on AB, we find %28AB%29%5E2+=+5%5E2%2B14%5E2+=+221
Using the distance formula on BC, we find %28BC%29%5E2+=+10%5E2+%2B+%2813-y%29%5E2

Then
221+=+100+%2B+%2813-y%29%5E2
121+=+%2813-y%29%5E2
11+=+13-y
y+=+2

Point C is (-7,2)