CPM Homework Help : CCG Problem 8-62

If $\Delta ABC$ is equilateral and if $A(0, 0)$ and $B(12, 0)$ , then what do you know about the coordinates of vertex $C$ ? Prove your answer is true.

Hint 1:

Notice the position of the third vertex for both triangles. They both have an $x$ -coordinate of $6$ .

Hint 2:

Use the patterns you learned for special right triangles to find the height of the congruent equilateral triangles.

Answer:

Vertex $C$ can be at $(6, 6\sqrt3)$ or $(6, -6\sqrt3)$ .

Use the eTool below to create your equilateral triangles.
Click the link at right for the full version of the eTool: 8-62 HW eTool