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)
|
|
|
