Question

Plot the given points on graph paper. Draw $\Delta \mathit{\text{FAT}}$. Locate point $\mathit{\text{C}}$so that role="math" localid="1638337170606" $\Delta \mathit{\text{FAT}}\cong \Delta \mathit{\text{CAT}}$.

role="math" localid="1638337180452" $\mathit{\text{F}}\left(\mathbf{7}\text{,}\mathbf{5}\right)$role="math" localid="1638337224388" $\mathit{\text{A}}\left(\text{-}\mathbf{2}\text{,}\mathbf{2}\right)$role="math" localid="1638337234009" $\mathit{\text{T}}\left(\mathbf{5}\text{,}\mathbf{2}\right)$

Short answer

Coordinate of $\mathit{\text{C}}$is $(7,-1)$.

Step-by-step solution

Step 1. Plot the diagram.

Plot $F\left(7,5\right),$$A\left(-2,2\right)$ and $T\left(5,2\right)$on the graph paper and draw $\Delta FAT$ as:

Step 2. Show the 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.

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

As, see $\overline{AT}$is common to both the triangles. Therefore point 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.

Step 3. State the conclusion.

Therefore, the coordinate of point $C$ is$\left(7,-1\right)$