Exercise 41 Page 550

Does the transformation preserve side lengths and angle measures?

Is the transformation a translation? No
Explanation: See solution.

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Let's start by drawing △ ABC.

The rule (x,y)→ (x + y,y) translates a point (x,y) to the right y units.

Translation	Simplify
A(2, 2) → A'(2 + 2,2)	A(2,2) → A'(4,2)
B(4, 2) → B'(4 + 2,2)	B(4,2) → B'(6,2)
C(3, 4) → C'(3 + 4,4)	C(3,4) → C'(7,4)

Let's plot A', B', and C' and draw the image.

We see that △ ABC and △ A'B'C' do not have the same side lengths and angle measures. Therefore, because a translation is a rigid motion that preserves side lengths and angle measures, we know that the given transformation is not a translation.

Subchapter links

Communicate Your Answer p.543

Monitoring Progress p.545-547

Exercises p.548-550

Exercise 41 Page 550

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