Subjects geometry

Transformations Congruence 0F1129

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1. **State the problem:** Chani starts with point $S(-8,6)$ and applies two transformations: a translation right 5 units, then a 180° rotation around the origin. 2. **Apply the translation right 5 units:** Translation right 5 units means adding 5 to the $x$-coordinate: $$(-8,6) \to (-8+5, 6) = (-3,6)$$ This matches Chani's first step: $S'(-3,6)$. 3. **Apply the 180° rotation around the origin:** A 180° rotation around the origin transforms any point $(x,y)$ to $(-x,-y)$. Applying this to $S'(-3,6)$: $$(-3,6) \to (3,-6)$$ 4. **Compare with Chani's second transformation:** Chani's result is $S''(-3,-6)$, but the correct result should be $(3,-6)$. 5. **Identify the mistake:** Chani's second point has the $x$-coordinate unchanged and the $y$-coordinate negated, which is the effect of reflecting over the $x$-axis, not a 180° rotation. **Final conclusion:** Chani reflected over the $x$-axis instead of performing a 180° rotation around the origin. **Answer:** Chani reflected over the x-axis instead of a 180 degree rotation around the origin.