SOLUTION: The vertices of the base of an isosceles triangle are at (1,2) and (4,-1). Determine the ordinate of the third vertex it its abscissa is 6.

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Question 166145: The vertices of the base of an isosceles triangle are at (1,2) and (4,-1). Determine the ordinate of the third vertex it its abscissa is 6.
Answer by Mathtut(3670) About Me  (Show Source):
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since (1,2) and (4,-1) are the vertices of the isosceles and the other vertex is (6,y) we know that the distance between (1,2) and the 3rd vertex will be equal to the distance between (4,-1) and the 3rd vertex.
using the distance formula sqrt%28%286-1%29%5E2%2B%28y-2%29%5E2%29=sqrt%28%286-4%29%5E2%2B%28y%2B1%29%29%5E2--->
square both sides to get rid of squareroot signs then simplify
25+y^2-4y+4=4+y^2+2y+1----->6y=24---y=4 so the 3rd vertex is (6,4)