1. **Problem Statement:** We have a quadrilateral QRST with given coordinates before and after a reflection. We need to describe the transformation, identify the algebraic rule, find the image of point T, and evaluate statements about another reflection. 2. **Step 1: Describe the transformation for QRST.** Looking at the points: - Q(-9, -8) maps to Q'(9, -8) - R(-9, -2) maps to R'(9, -2) - S(-4, -2) maps to S'(4, -2) The x-coordinates change sign from negative to positive, while y-coordinates remain the same. 3. **Step 2: Algebraic representation of the transformation.** The transformation changes $(x, y)$ to $(-x, y)$ if reflecting over the y-axis, but here the x changes from negative to positive, so the rule is $(x, y) \to (-x, y)$ applied to the pre-image points. Since the image points have positive x-values, the transformation is a reflection over the y-axis. 4. **Step 3: Find the location of T'.** Given T(-4, -8), applying the reflection over the y-axis: $$T' = (-(-4), -8) = (4, -8)$$ 5. **Step 4: Evaluate statements about the reflection in Section C.** - Statement 6: The pre-image is in quadrant III. - Quadrant III has negative x and y. The pre-image is in quadrant II (negative x, positive y), so this is **False**. - Statement 7: The orientation of the vertices changed. - Reflection preserves orientation, so this is **False**. - Statement 8: The reflection can be represented by $(-x, y)$. - The reflection in Section C is across the x-axis, so the rule is $(x, y) \to (x, -y)$, so this is **False**. - Statement 9: The line of reflection is the x-axis. - Given the reflection flips y-values, this is **True**. - Statement 10: The pre-image and image are congruent. - Reflections preserve size and shape, so this is **True**. **Final answers:** - 3. The transformation is a reflection over the y-axis. - 4. The algebraic rule is b. $(-x, y)$. - 5. $T' = (4, -8)$. - 6. False (pre-image is in quadrant II). - 7. False (orientation does not change). - 8. False (reflection is not $(-x, y)$ in Section C). - 9. True (line of reflection is the x-axis). - 10. True (pre-image and image are congruent).