Exercise 2 Page 580

We are given the vertices of a triangle and told how it is transformed. Let's see the vertices of this triangle before and after the given transformation. ccc Before & & After A(0,0) & ⟶ & A'(0,0) B(2,4) & ⟶ & B'(1,2) C(6,0) & ⟶ & C'(3,0) We want to know which of the following four transformations produced the image triangle.

Letter	Image	Transformation
a	Similar	A dilation with a scale factor of 12
b	Congruent	A 90^(∘) clockwise rotation about the origin
c	Congruent	A reflection across the x-axis
d	Similar	A translation of (x+1, y-3) followed by a dilation with a scale of 2

Let's graph both the original triangle and the image on the same coordinate plane.

The two triangles seem to be similar but not congruent. Let's focus on the two transformations in which the image is similar to the original triangle.

Letter	Image	Transformation
a	Similar	A dilation with a scale factor of 12
d	Similar	A translation of (x+1, y-3) followed by a dilation with a scale of 2

Next, notice that only point A remains unchanged after the transformation. Let's check whether point A remains unchanged during the transformation d. cc A( 0, 0) & ↓ & Translation of ( x+1, y-3) (1, -3) & ↓ & Dilation with a scale of 2 (2, -6) & Transformation d changes the position of point A. This means it cannot be the answer. Let's check the last candidate we have.

Letter	Image	Transformation
a	Similar	A dilation with a scale factor of 12

Let's check if this answer is correct. We can apply this transformation to the original triangle to see if the results match. Our transformation is correct!