### Home > CCG > Chapter 8 > Lesson 8.1.5 > Problem8-62

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.

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

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

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 (Desmos)