Question

reflections on the coordinate plane
#2. write an algebraic representation for the reflection. (-x, y)

Explanation:

Step1: Identify original triangle points

Original vertices: $I(-6, -7)$, $J(-1, -3)$, $K(-5, -2)$

Step2: Apply reflection rule $(-x,y)$

For $I$: $-(-6) = 6$, so $(6, -7)$
For $J$: $-(-1) = 1$, so $(1, -3)$
For $K$: $-(-5) = 5$, so $(5, -2)$

Step3: Confirm reflection axis

The rule $(-x, y)$ reflects over the $y$-axis, which matches flipping the triangle from left to right of the $y$-axis.

Answer:

The algebraic representation for the reflection is $\boldsymbol{(x, y) \to (-x, y)}$, which reflects the figure over the $y$-axis. The reflected vertices are $I'(6, -7)$, $J'(1, -3)$, $K'(5, -2)$.