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Answers without the blur. Sign up and see all textbooks for free! Q13.

Expert-verified Found in: Page 120 ### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279 # 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" $\mathit{\text{T}}\left(\mathbf{5}\text{,}\mathbf{2}\right)$

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

See the 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 $\left(7,-1\right)$ ### Want to see more solutions like these? 