Lesson 9-3: Similarity and Transformations — Practice Questions

1. 1. Which of the following best describes a similarity transformation in a plane?

   • A. A sequence of one or more rigid motions.
   • B. A sequence of rigid motions and/or dilations.
   • C. Any transformation that changes the area of a figure.
   • D. A sequence of one or more dilations.

2. 2. Triangle $XYZ$ is rotated $90^\circ$ and then dilated by a scale factor of $k=5$ to create triangle $X'Y'Z'$. Which statement is true?

   • A. $\Delta XYZ$ is congruent to $\Delta X'Y'Z'$.
   • B. $\Delta XYZ$ is similar to $\Delta X'Y'Z'$.
   • C. $\Delta XYZ$ is larger than $\Delta X'Y'Z'$.
   • D. The triangles are not similar.

3. 3. Polygon $ABCD$ is mapped to Polygon $A'B'C'D'$ using only a translation and a reflection. What can be concluded about the two polygons?

   • A. They are similar, but not congruent.
   • B. They are congruent, but not similar.
   • C. They are both congruent and similar.
   • D. They are neither congruent nor similar.

4. 4. A similarity transformation maps Polygon F to Polygon G. If the transformation includes a dilation with a scale factor of $k=1$, what must be true about the two polygons?

   • A. They are similar only.
   • B. They are congruent only.
   • C. They are both congruent and similar.
   • D. They are neither congruent nor similar.

5. 5. A pentagon is reflected across the y-axis and then dilated by a scale factor of $k = \frac{1}{3}$. How does the resulting pentagon relate to the original?

   • A. It is congruent and smaller.
   • B. It is similar and larger.
   • C. It is similar and smaller.
   • D. It is congruent and larger.

6. 6. Segment $XY$ is mapped to $X'Y'$ by a dilation with scale factor 4, followed by a translation $(x, y) \to (x+a, y+b)$. Given $X(3, 1)$ and its image $X'(10, 7)$, find the value of $a$. ___

7. 7. Segment $DE$ with $D(2, 3)$ is mapped to segment $D'E'$ with $D'(6, -9)$ by a dilation centered at the origin followed by a rigid transformation. The scale factor is 3. What is the rigid transformation?

   • A. A reflection across the x-axis
   • B. A reflection across the y-axis
   • C. A translation 3 units down
   • D. A rotation of 90 degrees

8. 8. Triangle $ABC$ is mapped to triangle $A'B'C'$ by a similarity transformation. If segment $AB$ has endpoints $A(1, 2)$ and $B(4, 2)$, and its image $A'B'$ has endpoints $A'(2, 4)$ and $B'(8, 4)$, what is the scale factor? ___

9. 9. Segment $PQ$ with endpoints $P(4, 2)$ and $Q(8, 2)$ is mapped to segment $P'Q'$ with endpoints $P'(-2, 1)$ and $Q'(-4, 1)$. Which sequence of transformations describes this mapping?

   • A. Dilation with scale factor $1/2$, then reflection across the y-axis.
   • B. Dilation with scale factor $2$, then reflection across the y-axis.
   • C. Dilation with scale factor $1/2$, then reflection across the x-axis.
   • D. Dilation with scale factor $2$, then translation 6 units left.

10. 10. Segment $A'B'$ is the image of segment $AB$ after a dilation centered at the origin. If $A(2, 3)$, $B(5, 3)$, $A'(3, 4.5)$, and $B'(7.5, 4.5)$, what is the scale factor of the dilation? ___