1. **State the problem:** We need to describe a sequence of rigid motions followed by a dilation with center at (0,0) that maps quadrilateral RSTU to VXYZ. 2. **Given points:** - RSTU: R(4,2), S(6,6), T(4,10), U(2,6) - VXYZ: V(-4,-2), X(-2,-6), Y(-4,-10), Z(-6,-6) 3. **Step 1: Identify the reflection.** - Notice that R(4,2) maps to V(-4,-2), which is the reflection of R across the origin. - Reflecting across the x-axis changes $(x,y)$ to $(x,-y)$. - Reflecting across the y-axis changes $(x,y)$ to $(-x,y)$. - Reflecting across the origin changes $(x,y)$ to $(-x,-y)$. Since the points move from positive x and y to negative x and y, reflection across the origin is equivalent to reflection across both axes. 4. **Step 2: Check translation.** - After reflection across the x-axis, R(4,2) would map to (4,-2). - To get to V(-4,-2), we need to translate left by 8 units. - After reflection across the y-axis, R(4,2) would map to (-4,2). - To get to V(-4,-2), we need to translate down by 4 units. - After reflection across the x-axis and translation right/up or left/down, check which matches the points. 5. **Step 3: Check scale factor for dilation.** - Distance from origin to R is $\sqrt{4^2 + 2^2} = \sqrt{20} \approx 4.47$. - Distance from origin to V is $\sqrt{(-4)^2 + (-2)^2} = \sqrt{20} \approx 4.47$. - Since distances are equal, scale factor is 1 (no dilation needed). 6. **Conclusion:** - Reflection across the x-axis maps R(4,2) to (4,-2). - Translation 8 units left moves (4,-2) to (-4,-2). - No dilation needed (scale factor 1). **Answer:** Choice A: Reflection across the y-axis, translation 0 units left and 0 units down, dilation with center (0,0) and scale factor 1 is incorrect. Choice B: Reflection across the x-axis, translation 8 units left and 0 units down, dilation with center (0,0) and scale factor 1 is correct. Choice C: Reflection across the x-axis, translation right and up is incorrect. Final sequence: Reflection across the x-axis, translation 8 units left and 0 units down, dilation with center (0,0) and scale factor 1.