Question

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

Short answer

Coordinate of $\mathit{\text{C}}$is $\left(7,2\right)$.

Step-by-step solution

Step 1. Plot the diagram.

Plot $F\left(1,2\right)$, $A\left(4,7\right)$ and $T\left(4,2\right)$ on the graph paper and draw $\Delta FAT$ as:

Step 2. Show the calculation.

Now, locate point $C$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:

Step 3. State the conclusion.

Therefore, the coordinate of point $C$ is$\left(7,2\right)$