Chapter 4.8, Problem 12PPS

To determine

The positioning and labelling of each triangle in coordinate plane.

Answer to Problem 12PPS

  

Explanation of Solution

Given:

Equilateral triangle DEF with sides 4b units long.

Calculation:

Locate the point D at the origin (0, 0).

Locate the points E at $\left(4b,0\right),\text{ such that }DE=4b.$

Locate the point F at $\left(2b,h\right),\text{ such that DF = EF}.$

  

Now,

  $\begin{array}{l}FD=DE\\ \sqrt{{\left(2b\right)}^2+h^2}=4b\\ 4b^2+h^2=16b^2\\ h^2=12b^2\\ h=2\sqrt{3}b\\ So,\text{ F is at }\left(2b,2\sqrt{3}b\right).\end{array}$