Chapter 4.1, Problem 13WE

To determine

To plot: the given points on graph paper, and to draw $\Delta FAT$ and to locate $C$ so that $\Delta FAT\cong \Delta CAT$ .

Answer to Problem 13WE

Point $C$ is $\left(7,-1\right)$ .

Explanation of Solution

Given information:

Given points,

  $F\left(7,5\right),A\left(-2,2\right),T\left(5,2\right)$

Calculation:

The two triangles are said to be congruent if they are copies of each other and if their vertices are superposed, then can say that the corresponding angles and the sides of the triangles are congruent.

Plot the given points on the graph paper as shown below:

  $F\left(7,5\right),A\left(-2,2\right),T\left(5,2\right)$

  

Now, to locate point $C$ so that $\Delta FAT\cong \Delta CAT$ .

As, see $\overline{AT}$ is common to both the triangles. Therefore point $C$ will be below $\overline{AT}$ . To reach point $F$ from point $T$ , move 2 boxes right and then, 3 boxes vertically above. In same manner to reach point $C$ from point $T$ , move 2 boxes right and then, 3 boxes vertically below.

Thus point $C$ is $\left(7,-1\right)$ .