Question

question
reflect the figure over the line $y = -1$.
plot all of the points of the reflected figure.
you may click a plotted point to delete it.

Explanation:

Step1: Identify original points

Original triangle points: $(-5, -6)$, $(-4, -8)$, $(-2, -8)$

Step2: Find reflection formula

For reflection over $y = k$, new $y$-coordinate: $y' = 2k - y$. Here $k=-1$, so $y' = 2(-1) - y = -2 - y$. $x$-coordinate stays same.

Step3: Calculate first reflected point

For $(-5, -6)$: $y' = -2 - (-6) = 4$. New point: $(-5, 4)$

Step4: Calculate second reflected point

For $(-4, -8)$: $y' = -2 - (-8) = 6$. New point: $(-4, 6)$

Step5: Calculate third reflected point

For $(-2, -8)$: $y' = -2 - (-8) = 6$. New point: $(-2, 6)$

Answer:

The reflected points are $(-5, 4)$, $(-4, 6)$, and $(-2, 6)$