document.write( "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.\r
\n" ); document.write( "\n" ); document.write( "Diagram: https://imgur.com/a/O9tws93 \n" ); document.write( "

Algebra.Com's Answer #769399 by greenestamps(13203) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "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.

\n" ); document.write( "(AB)^2 = 5^2+14^2 = 25+196 = 221
\n" ); document.write( "(BC)^2 = 10^2+(13-y)^2

\n" ); document.write( " $\"10%5E2%2B%2813-y%29%5E2+=+221\"$
\n" ); document.write( " $\"%2813-y%29%5E2+=+121\"$
\n" ); document.write( " $\"13-y+=+11\"$ or $\"13-y+=+-11\"$
\n" ); document.write( " $\"y+=+2\"$ or $\"y+=+24\"$

\n" ); document.write( "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.

\n" ); document.write( "ANSWER: C is (-7,24) \n" ); document.write( "

\n" );