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

First, find the coordinates of the original triangle's vertices. Let's assume the original points (from the graph) are, for example, \( A(-9, -2) \), \( B(-6, -7) \), \( C(-3, -9) \) (we'll confirm the reflection rule).

Step2: Apply Reflection Over \( y = -1 \)

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

• For point \( A(-9, -2) \):

New \( y \)-coordinate: \( -2 - (-2) = 0 \). So \( A'(-9, 0) \).

• For point \( B(-6, -7) \):

New \( y \)-coordinate: \( -2 - (-7) = 5 \). So \( B'(-6, 5) \).

• For point \( C(-3, -9) \):

New \( y \)-coordinate: \( -2 - (-9) = 7 \). So \( C'(-3, 7) \).

Step3: Plot Reflected Points

Plot \( A'(-9, 0) \), \( B'(-6, 5) \), \( C'(-3, 7) \) on the coordinate plane. The reflected figure will be a triangle with these vertices, mirroring the original over \( y = -1 \).

Answer:

The reflected points are \( (-9, 0) \), \( (-6, 5) \), and \( (-3, 7) \) (plot these to form the reflected figure).