Question

reflect the figure over the line $y = -2$. plot all of the points of the reflected figure. you may click a plotted point to delete it.

Explanation:

Step1: Identify original points

Original points: $(-8, -3)$, $(-6, -9)$, $(-3, -7)$, $(-3, -6)$, $(0, -4)$

Step2: Find reflection formula

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

Step3: Calculate reflected points

For $(-8, -3)$:

$y' = -4 - (-3) = -1$, so $(-8, -1)$

For $(-6, -9)$:

$y' = -4 - (-9) = 5$, so $(-6, 5)$

For $(-3, -7)$:

$y' = -4 - (-7) = 3$, so $(-3, 3)$

For $(-3, -6)$:

$y' = -4 - (-6) = 2$, so $(-3, 2)$

For $(0, -4)$:

$y' = -4 - (-4) = 0$, so $(0, 0)$

Answer:

The reflected points are $(-8, -1)$, $(-6, 5)$, $(-3, 3)$, $(-3, 2)$, $(0, 0)$ (plot these points to form the reflected figure)