Chapter 4.1, Problem 12WE

To determine

Toplot:Points $F\left(1,2\right),A\left(4,7\right)\text{and}T\left(4,2\right)$ on a graph paper and draw $\Delta FAT$ , also locate point C so that $\Delta FAT\cong \Delta CAT$ .

Answer to Problem 12WE

  $C\left(7,2\right)$

Explanation of Solution

Given:

  $F\left(1,2\right),A\left(4,7\right)\text{and}T\left(4,2\right)$

Calculation:

Plotting these $F\left(1,2\right),A\left(4,7\right)\text{and}T\left(4,2\right)$ points on graph paper and drawing $\Delta FAT$ as shown below.

  

Now, locating pointC at $\left(7,2\right)$ such that,

  $\begin{array}{l}FT\cong CT\\ \angle FTA=\angle CTA\\ TA=TA\end{array}$

By SAS congruence criteria, $\Delta FAT\cong \Delta CAT$ and are shown below.

  

Therefore, the coordinates of point Cis $\left(7,2\right)$ .