Question

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 triangle points: $(-7, 4)$, $(-4, 5)$, $(-2, 2)$

Step2: Reflection formula for $y=k$

For a point $(x,y)$, reflection over $y=k$ is $(x, 2k - y)$. Here $k=-2$, so formula is $(x, 2(-2)-y)=(x, -4 - y)$

Step3: Calculate reflected point 1

For $(-7, 4)$:
$x=-7$, $y=-4 - 4=-8$
Reflected point: $(-7, -8)$

Step4: Calculate reflected point 2

For $(-4, 5)$:
$x=-4$, $y=-4 - 5=-9$
Reflected point: $(-4, -9)$

Step5: Calculate reflected point 3

For $(-2, 2)$:
$x=-2$, $y=-4 - 2=-6$
Reflected point: $(-2, -6)$

Answer:

The reflected figure has points: $(-7, -8)$, $(-4, -9)$, $(-2, -6)$ (plot these points on the grid to form the reflected triangle)