A sequence of transformations maps $\triangle JKL$ with vertex $J(1, 2)$ to $\triangle J''K''L''$ with vertex $J''(-1, -5)$. Which sequence could be used?

A reflection across the y-axis, then a translation 7 units down.

A translation 7 units down, then a reflection across the x-axis.

A rotation $180^\circ$ about the origin, then a translation by $\langle 1, 3 \rangle$.

A reflection across the x-axis, then a reflection across the y-axis.

A reflection across the y-axis followed by a reflection across the x-axis maps Figure A to Figure A''. Which single transformation achieves the same result?

A rotation of $90^\circ$ clockwise about the origin

A rotation of $180^\circ$ about the origin

A reflection across the line $y = x$

A translation by the vector $\langle 1, 1 \rangle$

Rigid Transformations Practice — Grade 8 math

Lesson 1: Rigid Transformations — Practice Questions

1. A sequence of transformations maps $\triangle JKL$ with vertex $J(1, 2)$ to $\triangle J''K''L''$ with vertex $J''(-1, -5)$. Which sequence could be used?
- A. A reflection across the y-axis, then a translation 7 units down.
- B. A translation 7 units down, then a reflection across the x-axis.
- C. A rotation $180^\circ$ about the origin, then a translation by $\langle 1, 3 \rangle$.
- D. A reflection across the x-axis, then a reflection across the y-axis.
2. Point $M(-4, 5)$ is translated 6 units right, then reflected across the x-axis. What are the coordinates of the final image $M''$? Enter your answer in the format (x, y).
3. A reflection across the y-axis followed by a reflection across the x-axis maps Figure A to Figure A''. Which single transformation achieves the same result?
- A. A rotation of $90^\circ$ clockwise about the origin
- B. A rotation of $180^\circ$ about the origin
- C. A reflection across the line $y = x$
- D. A translation by the vector $\langle 1, 1 \rangle$
4. A sequence of transformations maps $\triangle ABC$ with vertex $A(5, 8)$ to $\triangle A''B''C''$ with vertex $A''(-5, -3)$. The sequence is a reflection across the y-axis followed by a translation of ___ units down.
5. Consider two transformations. Transformation 1: a translation 5 units up. Transformation 2: a reflection across the x-axis. Does applying T1 then T2 produce the same result as applying T2 then T1?
- A. Yes
- B. No
6. Point $Q(3, -7)$ is rotated $90^\circ$ counter-clockwise about the origin, then translated by the vector $\langle -2, 4 \rangle$. What are the coordinates of the final image $Q''$? Enter your answer in the format (x, y).
7. A sequence of transformations maps point $D(-8, 2)$ to $D''(4, -2)$. The sequence consists of a translation 12 units right, followed by a reflection across the ___-axis.
8. Point $A(5, -2)$ is first translated by the vector $\langle -6, 3 \rangle$ to get $A'$. Then, $A'$ is reflected across the y-axis to get $A''$. What are the coordinates of $A''$? Enter as `(x, y)`.
9. A point $M(-4, 1)$ is reflected across the x-axis to get $M'$. Then, $M'$ is translated by vector $\langle h, 5 \rangle$ to get $M''(2, 4)$. What is the value of $h$? ___
10. Let $T$ be a translation by $\langle 3, 0 \rangle$ and $R_y$ be a reflection across the y-axis. If point $P$ is $(2, 4)$, are the images from $(T \circ R_y)(P)$ and $(R_y \circ T)(P)$ the same?
- A. Yes, the final images are the same.
- B. No, the final images are different.
- C. It is impossible to determine.
- D. The images are the same only because the x-coordinate is 2.