1. **Problem Statement:** Translate the polygon with vertices D(0,4), E(-3,-1), F(1,-5), and G(1,0) 3 units right and 3 units up. 2. **Translation Matrix:** Translation moves points by adding the translation vector to each vertex coordinate. Here, the translation vector is (3,3). 3. **Apply Translation:** - D'(0+3,4+3) = (3,7) - E'(-3+3,-1+3) = (0,2) - F'(1+3,-5+3) = (4,-2) - G'(1+3,0+3) = (4,3) 4. **Answer for #10:** The translated vertices are D'(3,7), E'(0,2), F'(4,-2), G'(4,3). --- 1. **Problem Statement:** Dilate the polygon with vertices W(1,2), X(-2,3), Y(-3,4), and Z(-4,1) by a factor of $\frac{3}{2}$. 2. **Dilation Matrix:** Dilation scales each coordinate by the factor $\frac{3}{2}$. 3. **Apply Dilation:** - W'(1 \times \frac{3}{2}, 2 \times \frac{3}{2}) = (1.5, 3) - X'(-2 \times \frac{3}{2}, 3 \times \frac{3}{2}) = (-3, 4.5) - Y'(-3 \times \frac{3}{2}, 4 \times \frac{3}{2}) = (-4.5, 6) - Z'(-4 \times \frac{3}{2}, 1 \times \frac{3}{2}) = (-6, 1.5) 4. **Answer for #11:** The dilated vertices are W'(1.5,3), X'(-3,4.5), Y'(-4.5,6), Z'(-6,1.5). --- 1. **Problem Statement:** Reflect the figure with vertices A(-2,3), B(0,4), C(2,3), D(2,1), and E(-1,-1) across the x-axis. 2. **Reflection Matrix:** Reflection across the x-axis changes $(x,y)$ to $(x,-y)$. 3. **Apply Reflection:** - A'(-2, -3) - B'(0, -4) - C'(2, -3) - D'(2, -1) - E'(-1, 1) 4. **Answer for #12:** The reflected vertices are A'(-2,-3), B'(0,-4), C'(2,-3), D'(2,-1), E'(-1,1). --- 1. **Problem Statement:** Rotate the figure PQRST with vertices P(-3,2), Q(0,0), R(-4,1), S(-4,4), and T(-1,4) using the matrix $\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$. 2. **Rotation Matrix Explanation:** This matrix rotates points 90° counterclockwise about the origin. 3. **Apply Rotation:** - P' = $(0 \times -3 + -1 \times 2, 1 \times -3 + 0 \times 2) = (-2, -3)$ - Q' = $(0 \times 0 + -1 \times 0, 1 \times 0 + 0 \times 0) = (0, 0)$ - R' = $(0 \times -4 + -1 \times 1, 1 \times -4 + 0 \times 1) = (-1, -4)$ - S' = $(0 \times -4 + -1 \times 4, 1 \times -4 + 0 \times 4) = (-4, -4)$ - T' = $(0 \times -1 + -1 \times 4, 1 \times -1 + 0 \times 4) = (-4, -1)$ 4. **Answer for #13:** The rotated vertices are P'(-2,-3), Q'(0,0), R'(-1,-4), S'(-4,-4), T'(-4,-1). --- 1. **Problem Statement:** Rotate the figure PQRST with vertices P(-3,2), Q(0,0), R(-4,1), S(-4,4), and T(-1,4) using the matrix $\begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix}$. 2. **Rotation Matrix Explanation:** This matrix rotates points 90° clockwise about the origin. 3. **Apply Rotation:** - P' = $(0 \times -3 + 1 \times 2, -1 \times -3 + 0 \times 2) = (2, 3)$ - Q' = $(0 \times 0 + 1 \times 0, -1 \times 0 + 0 \times 0) = (0, 0)$ - R' = $(0 \times -4 + 1 \times 1, -1 \times -4 + 0 \times 1) = (1, 4)$ - S' = $(0 \times -4 + 1 \times 4, -1 \times -4 + 0 \times 4) = (4, 4)$ - T' = $(0 \times -1 + 1 \times 4, -1 \times -1 + 0 \times 4) = (4, 1)$ 4. **Answer for #14:** The rotated vertices are P'(2,3), Q'(0,0), R'(1,4), S'(4,4), T'(4,1).