reflect the figure over the line $y = -2$. plot all of the points of the reflected figure. you may click a…

Explanation:

Step1: Identify original points

Original vertices: $(-8, -3)$, $(-7, -9)$, $(-2, -7)$, $(-3, -6)$, $(-1, -4)$

Step2: Apply reflection formula

For a point $(x,y)$ reflected over $y=k$, new $y$-coordinate: $y' = 2k - y$. Here $k=-2$, so $y' = 2(-2)-y = -4 - y$. $x$-coordinate stays same.

For $(-8, -3)$:

$y' = -4 - (-3) = -1$, new point: $(-8, -1)$

For $(-7, -9)$:

$y' = -4 - (-9) = 5$, new point: $(-7, 5)$

For $(-2, -7)$:

$y' = -4 - (-7) = 3$, new point: $(-2, 3)$

For $(-3, -6)$:

$y' = -4 - (-6) = 2$, new point: $(-3, 2)$

For $(-1, -4)$:

$y' = -4 - (-4) = 0$, new point: $(-1, 0)$

Answer:

The reflected figure's vertices are $(-8, -1)$, $(-7, 5)$, $(-2, 3)$, $(-3, 2)$, $(-1, 0)$