reflect the figure over the line $y = -1$. plot all of the points of the reflected figure. you may click a…

Explanation:

Step1: Identify Original Points

First, find the coordinates of the original triangle's vertices. From the graph, the points are: ( A(-4, -4) ), ( B(-1, -4) ), ( C(-2, -8) ).

Step2: Reflect Over ( y = -1 )

The formula for reflecting a point ( (x, y) ) over the horizontal line ( y = k ) is ( (x, 2k - y) ). Here, ( k = -1 ), so the reflection formula becomes ( (x, 2(-1) - y) = (x, -2 - y) ).

For Point ( A(-4, -4) ):

Substitute ( x = -4 ), ( y = -4 ) into the formula:
( y' = -2 - (-4) = -2 + 4 = 2 ).
Reflected point: ( A'(-4, 2) ).

For Point ( B(-1, -4) ):

Substitute ( x = -1 ), ( y = -4 ):
( y' = -2 - (-4) = 2 ).
Reflected point: ( B'(-1, 2) ).

For Point ( C(-2, -8) ):

Substitute ( x = -2 ), ( y = -8 ):
( y' = -2 - (-8) = -2 + 8 = 6 ).
Reflected point: ( C'(-2, 6) ).

Step3: Plot Reflected Points

Plot ( A'(-4, 2) ), ( B'(-1, 2) ), and ( C'(-2, 6) ) on the coordinate plane.

Answer:

The reflected figure has vertices at ((-4, 2)), ((-1, 2)), and ((-2, 6)) (plotted on the graph as described).