SOLUTION: The equilateral triangle is one in which all three sides are of equal length. If two vertices of an equilateral triangle are (0,4) and (0,0), find the third vertex.

Question 380119: The equilateral triangle is one in which all three sides are of equal length.
If two vertices of an equilateral triangle are (0,4) and (0,0), find the third vertex.
Found 2 solutions by richard1234, robertb:
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
It is clear that the side length of the triangle is 4. However there are two possible vertices -- (2sqrt(3), 2) and (-2sqrt(3), 2). Graph it on a coordinate plane and you'll see that both triangles are equilateral.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Note that the two vertices are located on the y-axis. Thus the y coordinate of the 3rd vertex must be midway between 0 and 4, i.e., y = 2. Hence the 3rd vertex is (x,2), where x is unknown.
Now the triangle with vertices (0,0), (0,2), and (x,2) is a 30-60-90 triangle, and so must have hypotenuse 4, shortest leg 2, and middle leg , by property of that triangle. The 3rd vertx is then(, 2).
Therefore there are two possible 3rd vertices: (, 2), or (, 2)

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