Question

reflect the figure over the line y = -x - 1. plot all of the points of the reflected figure. you may click a plotted point to delete it.

Explanation:

Step1: Identify original vertices

Assume original triangle vertices: \( A(1,2) \), \( B(4,8) \), \( C(7,8) \)

Step2: Reflection formula for \( y=-x-1 \)

For point \( (x,y) \), reflected point \( (x',y') \) is \( x'=-y-1 \), \( y'=-x-1 \)

Step3: Reflect \( A(1,2) \)

\( x'=-2-1=-3 \), \( y'=-1-1=-2 \) → \( A'(-3,-2) \)

Step4: Reflect \( B(4,8) \)

\( x'=-8-1=-9 \), \( y'=-4-1=-5 \) → \( B'(-9,-5) \)

Step5: Reflect \( C(7,8) \)

\( x'=-8-1=-9 \), \( y'=-7-1=-8 \) → \( C'(-9,-8) \)

Answer:

Reflected vertices: (-3,-2), (-9,-5), (-9,-8)