1. Problem: Write a reflection rule that maps each triangle to its image. 2. Reflection rule means finding the line or axis over which the triangle is flipped. 3. For part a: Points J(1,0), K(-5,2), L(4,-4) map to J'(-9,0), K'(-3,2), L'(-12,-4). 4. Notice the y-coordinates do not change, only x-coordinates change. 5. Calculate midpoint of J and J': $$\left(\frac{1 + (-9)}{2}, \frac{0 + 0}{2}\right) = (-4, 0)$$ 6. Midpoint is on the reflection line, so the reflection line is vertical at $$x = -4$$. 7. So the reflection rule is: Reflect over the vertical line $$x = -4$$. 8. For part b: Points P(8,6), Q(-4,12), R(7,7) map to P'(8,-20), Q'(-4,-26), R'(7,-21). 9. Notice x-coordinates stay the same, y-coordinates change. 10. Calculate midpoint of P and P': $$\left(\frac{8 + 8}{2}, \frac{6 + (-20)}{2}\right) = (8, -7)$$ 11. Midpoint lies on the reflection line, so the reflection line is horizontal at $$y = -7$$. 12. So the reflection rule is: Reflect over the horizontal line $$y = -7$$. Final answers: - a) Reflection over the line $$x = -4$$. - b) Reflection over the line $$y = -7$$.