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

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


   

Question 1148033: Acute isosceles triangle ABC has vertices A(-2,-1), B(3,13), with point C on the line x= -7. If line AB=line BC, the find the coordinates of point C.
Diagram: https://imgur.com/a/O9tws93
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


We want the lengths AB and CB to be the same. Using the distance formula (aka Pythagorean Theorem), we can use the squares of the lengths.

(AB)^2 = 5^2+14^2 = 25+196 = 221
(BC)^2 = 10^2+(13-y)^2

10%5E2%2B%2813-y%29%5E2+=+221
%2813-y%29%5E2+=+121
13-y+=+11 or 13-y+=+-11
y+=+2 or y+=+24

We used the squares of the lengths, so one of those solutions is extraneous. A glance at the diagram shows the y value we want is 24.

ANSWER: C is (-7,24)