Question

for exercise 8, select all statements that are true. 8. consider the graph of △abc and its image, △abc. which of the statements is accurate regarding the transformation shown? select all that apply. (lesson 2) a. △abc is the image of a reflection of △abc across the x - axis. b. △abc is the image of a reflection of △abc across the y - axis. c. the x - coordinates of the vertices of △abc and its image △abc are the same. d. the x - coordinates of the vertices of △abc and its image △abc are opposites. e. the y - coordinates of the vertices of △abc and its image △abc are the same. f. the y - coordinates of the vertices of △abc and its image △abc are opposites.

Explanation:

Step1: Recall reflection rules

A reflection across the y - axis changes the sign of the x - coordinate of each point while keeping the y - coordinate the same. That is, if a point has coordinates $(x,y)$ its image after reflection across the y - axis has coordinates $(-x,y)$.

Step2: Analyze the graph

In the given graph, $\triangle A'B'C'$ is the image of $\triangle ABC$ across the y - axis. For example, if point $A$ has coordinates $(x_1,y_1)$, point $A'$ has coordinates $(-x_1,y_1)$. The x - coordinates of the corresponding vertices of $\triangle ABC$ and $\triangle A'B'C'$ are opposites and the y - coordinates are the same.

Answer:

B. $\triangle A'B'C'$ is the image of a reflection of $\triangle ABC$ across the y - axis.
D. The x - coordinates of the vertices of $\triangle ABC$ and its image $\triangle A'B'C'$ are opposites.
E. The y - coordinates of the vertices of $\triangle ABC$ and its image $\triangle A'B'C'$ are the same.