<PRE><B>Question 1205117</B>
&lt;br&gt;
AC and BC are the congruent sides, so the third side is AB.&lt;br&gt;
If M is the midpoint of AB, then MC is the altitude of the triangle.&lt;br&gt;
The midpoint of AB is (2,-1).
The slope of AB is -1/2.
The slope of MC (the altitude to AB) is the negative reciprocal of the slope of AB: 2.
The equation of the altitude MC -- with slope 2 and passing through (2,-1) -- is y=2x-5.&lt;br&gt;
I leave it to the student to fill in the details for the above calculations.&lt;br&gt;
The intersection of MC and the given line is the point C whose coordinates we are to find.  With the two equations in the form we have, solve using substitution:&lt;br&gt;
{{{4x-7y+15=0}}}; {{{y=2x-5}}}
{{{4x-7(2x-5)+15=0}}}
{{{4-14x+35+15=0}}}
{{{50=10x}}}
{{{x=5}}}&lt;br&gt;
{{{y=2x-5=10-5=5}}}&lt;br&gt;
ANSWER: (5,5)&lt;br&gt;
</PRE>