Question

show how each vertex of △efg maps to its image. describe in words how to map △efg to its image △efg using a reflection. complete the table with the coordinates of the image points e, f, and g. (type ordered pairs.) which statement below describes the reflection? a. △efg is the image of △efg after a reflection across the line x = 1 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 y - axis 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 y - axis, the rule is $(x,y)\to(-x,y)$. For a reflection across the x - axis, the rule is $(x,y)\to(x, - y)$. For a reflection across the line $x = a$, the rule is $(x,y)\to(2a - x,y)$ and for a reflection across the line $y = b$, the rule is $(x,y)\to(x,2b - y)$.

Step2: Analyze the coordinates of $\triangle EFG$ and $\triangle E'F'G'$

The coordinates of $\triangle EFG$ are $E(-3,5)$, $F(-2,4)$, $G(-4,3)$ and of $\triangle E'F'G'$ are $E'( - 1,5)$, $F'(0,4)$, $G'(2,3)$. The x - coordinates of the points in $\triangle EFG$ change according to the rule $(x,y)\to(2\times1 - x,y)$ when reflected across the line $x = 1$. For example, for point $E(-3,5)$, $2\times1-(-3)=2 + 3=5$.

Step3: Determine the correct option

The transformation from $\triangle EFG$ to $\triangle E'F'G'$ is a reflection across the line $x = 1$.

Answer:

A. $\triangle E'F'G'$ is the image of $\triangle EFG$ after a reflection across the line $x = 1$