Question

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Describe the transformation from ΔABC to ΔA'B'C'. Is this a congruence or similarity transformation?

ΔABC: A(-3, 3), B(-3, 1)
ΔA'B'C': A'(6, 6), B'(6, 2), C'(2, 2)

Answer 1

Dilation of scale factor 2 centered at the origin, followed by a reflection in the y-axis.

Similarity transformation.

Explanation:

Given vertices of ΔABC:

• A = (-3, 3)
• B = (-3, 1)
• C = (-1, 1)

Given vertices of ΔA'B'C':

• A' = (6, 6)
• B' = (6, 2)
• C' = (2, 2)

From observation, the series of transformations the transforms ΔABC to ΔA'B'C' are:

• Dilation of scale factor 2 centered at the origin.
• Reflection in the y-axis.

This is a similarity transformation as the two triangles have the same shape but different sizes.

Answer 2

From the coordinates we can see the rule for this transformation is:

• (x, y) → (-2x, 2y)

It is a dilation by a scale factor of 2 and reflection in the y-axis.

It means this is a similarity transformation, since the figure has changed its size.