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Q13.

Expert-verified

Geometry

Found in: Page 120

Book edition Student Edition

Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages 227 pages

ISBN 9780395977279

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Short Answer

Plot the given points on graph paper. Draw $Δ FAT$ . Locate point $C$ so that role="math" localid="1638337170606" $Δ FAT ≅ Δ CAT$ .
role="math" localid="1638337180452" $F (7, 5)$ role="math" localid="1638337224388" $A (- 2, 2)$ role="math" localid="1638337234009" $T (5, 2)$

Coordinate of $C$ is $(7, - 1)$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Plot the diagram.

Plot $F (7, 5),$ $A (- 2, 2)$ and $T (5, 2)$ on the graph paper and draw $Δ F A T$ 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 $Δ F A T ≅ Δ C A T$ .

As, see $\bar{A T}$ is common to both the triangles. Therefore point will be below $\bar{A T}$ . 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 $(7, - 1)$

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