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. From the graph, the points are: \( (2, 7) \), \( (8, 5) \), and \( (7, 2) \).

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 new \( y \)-coordinate is \( 2(-1) - y = -2 - y \).

• For \( (2, 7) \): New \( y = -2 - 7 = -9 \), so reflected point is \( (2, -9) \).
• For \( (8, 5) \): New \( y = -2 - 5 = -7 \), so reflected point is \( (8, -7) \).
• For \( (7, 2) \): New \( y = -2 - 2 = -4 \), so reflected point is \( (7, -4) \).

Step3: Plot Reflected Points

Plot the points \( (2, -9) \), \( (8, -7) \), and \( (7, -4) \) on the coordinate plane.

Answer:

The reflected figure has vertices at \( (2, -9) \), \( (8, -7) \), and \( (7, -4) \). (These points should be plotted on the graph as per the reflection rules.)