Question

Triangle ABC has vertices A(−3, 1), B(−3, 4), and C(−7, 1).

Answer 1

The solution to the questions are

• The description of the translation in words is horizontal shift to the left  by 4 units and vertical shift up by 3 units
• A(−7, 4), B(−7, 7), and C(−11, 5).
• ∆ABC is congruent to ∆A"B"C"

Part A: How is the translation described with words?

We have the translation to be:

∆ABC is translated according to the rule (x, y) → (x − 4, y + 3) to form ∆A'B'C'

The translation rule (x, y) → (x − 4, y + 3) involves a horizontal translation and a vertical translation

So, the description of the translation in words is horizontal shift to the left  by 4 units and vertical shift up by 3 units

Part B: Where are the vertices of ∆A'B'C' located?

We have:

A(−3, 1), B(−3, 4), and C(−7, 1).

When the rule applied, the points become

A(−7, 4), B(−7, 7), and C(−11, 5).

Part C: Is ∆ABC congruent to ∆A"B"C"?

Here, the transformation rule is given as:

Triangle A'B'C' is rotated 90° clockwise about the origin to form ∆A"B"C"

A clockwise rotation by 90° is a rigid transformation

This means that the sides and angles of both shapes are congruent

Hence, ∆ABC is congruent to ∆A"B"C"

Read more about transformation at:

brainly.com/question/4289712

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