CPM Homework Help : INT2 Problem 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.

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:

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

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