### Home > INT2 > Chapter 12 > Lesson 12.2.1 > Problem12-62

12-62.

If $ΔABC$ is equilateral and if $A(0, 0)$ and $B(12, 0)$, then what do you know about the coordinates of vertex $C$? Justify your solution in detail.

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.

$\text{Vertex }C\text{ can be at }(6,6\sqrt{3})\text{ or }(6,-6\sqrt{3}).$

Use the eTool below to create your equilateral triangles.
Click the link at right for the full version of the eTool: 12-62 HW eTool