SOLUTION: the vertices of the base of an isosceles triangle are at (1,2) and (4,-1). If the abscissa of the third vertex is 6, find its ordinate. Thank you!! God Bless!!

Algebra ->  Length-and-distance -> SOLUTION: the vertices of the base of an isosceles triangle are at (1,2) and (4,-1). If the abscissa of the third vertex is 6, find its ordinate. Thank you!! God Bless!!      Log On


   

Question 892474: the vertices of the base of an isosceles triangle are at (1,2) and (4,-1). If the abscissa of the third vertex is 6, find its ordinate.

Thank you!! God Bless!!
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You want your unknown point (6,y) to be the same distance from (1,2) as it is from (4,-1).
The segments, (6,y) to (1,2), and (6,y) to (4,-1), are the two equal sides of the isosceles
triangle.

sqrt%28%286-1%29%5E2%2B%28y-2%29%5E2%29=sqrt%28%286-4%29%5E2%2B%28y-%28-1%29%29%5E2%29
sqrt%28%285%29%5E2%2B%28y-2%29%5E2%29=sqrt%28%282%29%5E2%2B%28y%2B1%29%5E2%29
sqrt%2825%2B%28y-2%29%5E2%29=sqrt%284%2B%28y%2B1%29%5E2%29
%28y-2%29%5E2%2B25=%28y%2B1%29%5E2%2B4
y%5E2-4y%2B4%2B25=y%5E2%2B2y%2B1%2B4, see y%5E2 on both sides
-4y%2B29=2y%2B5
-6y%2B29=5
-6y=5-29
6y=29-5
6y=24
highlight%28y=4%29 --------the ordinate, or y value for the vertex opposite of the base.