SOLUTION: 18)a.The two vertices that form a non-congruent side of an isosceles triangle are (-5,3) and (2,3). What are the coordinates of the other vertex? b.The coordinates of the endpoi

Algebra ->  Triangles -> SOLUTION: 18)a.The two vertices that form a non-congruent side of an isosceles triangle are (-5,3) and (2,3). What are the coordinates of the other vertex? b.The coordinates of the endpoi      Log On


   

Question 1005156: 18)a.The two vertices that form a non-congruent side of an isosceles triangle are (-5,3) and (2,3). What are the coordinates of the other vertex?
b.The coordinates of the endpoints of the hypotenuse of a right triangle are (7,5) and (3,1). Find the other vertex. There are two possible solutions.

Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Question #a,
The set of points for the solution is a line perpendicular to the base of the triangle and containing the midpoint of the endpoints of the base. There will be two points on this line which are not the solution because either of them will form an equilateral triangle.


m=%283-3%29%2F%282%2B5%29=0, base being a horizontal segment.

x=-3%2F2, the line which contains the possible needed vertex.
A point which is NOT part of the solution is (-3/2,3), because this would not be a triangle.

The length of the base is 7 units. This means (-5+3/2)^2+(3-y)^2=7 and (2+3/2)^2+(3-y)^2=7 must not be part of the solution. You can find those prohibited values using arithmetic; the reason for the restriction is they would make an equilateral instead of isosceles triangle.