High School Transformations: Translations Test Questions with Solutions

📚 Quick Study Guide

• 🗺️ Translation Definition: A translation is a transformation that slides a figure without changing its size, shape, or orientation.
• ➡️ Translation Vector: A translation can be described by a vector $\begin{pmatrix} a \\ b \end{pmatrix}$, where $a$ represents the horizontal shift and $b$ represents the vertical shift.
• ➕ Positive a: Shifts the figure to the right.
• ➖ Negative a: Shifts the figure to the left.
• ⬆️ Positive b: Shifts the figure upwards.
• ⬇️ Negative b: Shifts the figure downwards.
• 📐 Coordinate Notation: If a point $(x, y)$ is translated by $\begin{pmatrix} a \\ b \end{pmatrix}$, the new point is $(x + a, y + b)$.

🤔 Practice Quiz

1. What is the image of the point $(3, -2)$ under the translation $\begin{pmatrix} -1 \\ 4 \end{pmatrix}$?
   1. (2, 2)
   2. (4, 2)
   3. (2, -6)
   4. (4, -6)
2. A triangle has vertices $A(1, 1)$, $B(3, 1)$, and $C(3, 3)$. If the triangle is translated by $\begin{pmatrix} -2 \\ -1 \end{pmatrix}$, what are the coordinates of $A'$?
   1. (3, 2)
   2. (-1, 0)
   3. (5, 2)
   4. (1, 1)
3. Which translation maps the point $(5, -3)$ to $(2, 1)$?
   1. $\begin{pmatrix} 3 \\ -4 \end{pmatrix}$
   2. $\begin{pmatrix} -3 \\ 4 \end{pmatrix}$
   3. $\begin{pmatrix} 7 \\ -2 \end{pmatrix}$
   4. $\begin{pmatrix} -7 \\ 2 \end{pmatrix}$
4. The point $(-4, 6)$ is translated to $(1, 8)$. What is the translation vector?
   1. $\begin{pmatrix} -5 \\ -2 \end{pmatrix}$
   2. $\begin{pmatrix} 5 \\ 2 \end{pmatrix}$
   3. $\begin{pmatrix} -3 \\ 14 \end{pmatrix}$
   4. $\begin{pmatrix} -5 \\ -14 \end{pmatrix}$
5. If the translation $\begin{pmatrix} 2 \\ -5 \end{pmatrix}$ maps point $P$ to $(7, -3)$, what are the coordinates of point $P$?
   1. (9, -8)
   2. (5, 2)
   3. (5, -8)
   4. (9, 2)
6. A square with vertices $(0, 0)$, $(2, 0)$, $(2, 2)$, and $(0, 2)$ is translated by $\begin{pmatrix} -1 \\ 3 \end{pmatrix}$. What are the coordinates of the translated square's vertices?
   1. (-1, 3), (1, 3), (1, 5), (-1, 5)
   2. (1, -3), (-1, -3), (-1, -5), (1, -5)
   3. (3, -1), (5, -1), (5, -3), (3, -3)
   4. (-1, -3), (1, -3), (1, -5), (-1, -5)
7. The line $y = 2x + 1$ is translated by $\begin{pmatrix} 1 \\ -3 \end{pmatrix}$. What is the equation of the translated line?
   1. $y = 2x - 4$
   2. $y = 2x + 4$
   3. $y = 2x - 6$
   4. $y = 2x + 6$