Question 1148033
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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.<br>
(AB)^2 = 5^2+14^2 = 25+196 = 221
(BC)^2 = 10^2+(13-y)^2<br>
{{{10^2+(13-y)^2 = 221}}}
{{{(13-y)^2 = 121}}}
{{{13-y = 11}}} or {{{13-y = -11}}}
{{{y = 2}}} or {{{y = 24}}}<br>
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.<br>
ANSWER: C is (-7,24)