SOLUTION: Two vertices of an equilateral triangle are (10,-4)and (0,6) the third vertex can be

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Question 1004282: Two vertices of an equilateral triangle are (10,-4)and (0,6) the third vertex can be
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Draw the line connecting the two points:



That's one side of the triangle.  The third vertex can be any point
that is NOT on the line through those two points. For instance, it
could be the vertex indicated by the green lines on the graphs below.


 
However it could not be anywhere on the line through the two 
given points.



To answer the question, we must find the equation of the line
through those points, i.e., the line that includes as a segment
one of the sides of the triangle.  To find the equation of that
line we use the slope formula to find its slope:

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

m=%28%286%29-%28-4%29%29%2F%28%280%29-%2810%29%29

m=%286%2B4%29%2F%28-10%29

m=10%2F%28-10%29

m=-1

The use the point-slope formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29

y-%28-4%29=%28-1%29%28x-%2810%29%5E%22%22%29

y%2B4=-%28x-10%29

y%2B4=-x%2B10

y=-x%2B6

Answer:  The third vertex can be any ordered
pair of this set:
 
 

Edwin