Question

error analysis your friend incorrectly says that the reflection of △efg to its image △efg is a reflection across the x - axis. what is the correct reflection? what is your friends mistake? what is the correct description of the reflection? a. △efg is the image of △efg after a reflection across the line y = - 5 b. △efg is the image of △efg after a reflection across the x - axis c. △efg is the image of △efg after a reflection across the line x = - 1 d. △efg is the image of △efg after a reflection across the line y = - 1

Explanation:

Step1: Recall reflection rules

For a reflection across the x - axis, the rule is (x,y)→(x, - y). For a reflection across the line y = k, the rule is (x,y)→(x,2k - y). For a reflection across the line x = h, the rule is (x,y)→(2h - x,y).

Step2: Analyze the graph

By observing the graph of △EFG and △E'F'G', we can see that the x - coordinates of the corresponding vertices remain the same and the y - coordinates change in a way that is consistent with a reflection across the line y=-1. If a point (x,y) is reflected across the line y = - 1, the new point is (x,-2 - y).

Answer:

D. △E'F'G' is the image of △EFG after a reflection across the line y=-1