SOLUTION: The two vertices that form the non-congruent side of an isosceles triangle are (-5,3) and (2,3). What are the coordinates of the other vertex. I am beyond lost. Thanks!

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Question 982117: The two vertices that form the non-congruent side of an isosceles triangle are (-5,3) and (2,3). What are the coordinates of the other vertex.
I am beyond lost. Thanks!
Found 3 solutions by josgarithmetic, macston, Edwin McCravy:
Answer by josgarithmetic(39792)   (Show Source): You can put this solution on YOUR website!
Look at the points on a cartesian coordinate system. They show the endpoints of the base of the isosceles triangle. The other vertex would be on the y-axis and would be the center of a circle. Notice that the given points form the segment of the triangle parallel to the x-axis. This makes identifying the point on the x-axis to be easy. Look for the midpoint of x coordinates of -5 and 2.



The vertex is ( -3/2, 0 ).
Answer by macston(5194)   (Show Source): You can put this solution on YOUR website!
The other vertex that forms the triangle is on a line perpendicular to the segment at its midpoint.
.
Find the midpoint:
midpoint=((x1+x2)/2,((y1+y2)/2)
midpoint=((-5+2)/2,(3+3)/2)
midpoint=(-(3/2),3)
.
Find the slope of the original segment:
m=slope
m=(y2-y1)/x2-x1
m=(3-3)/(2-(-5)=0/7=0
The line is horizontal.
.
The perpendicular line will be vertical, thus will have an undefined slope.
.
Equation for original line:
y=mx+b
y=3
.
The vertical line through the midpoint is x=-(3/2)
Any point on the line x=-(3/2) except (-(3/2),3) can be connected to the given vertices to form an isosceles triangle.
Answer by Edwin McCravy(20077)   (Show Source): You can put this solution on YOUR website!
The first tutor gave one possible solution, but there are infinitely many possible answers.

(-1.5,5), (-1.5,7), (-1.5,0), (-1.5,100), (-1.5,-100), etc.

the x-coordinate can only be -1.5, but the y-coordinate can be any number
except the two values that produce an equilateral triangle, since there are
no non-congruent sides to an equilateral triangle.  Here are 4 solutions.
The last one is the one the first tutor gave. 

  

  

Edwin
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