Question

6.2.ap-4 reasoning one image of δabc is δabc how do the x-coordinates of the vertices change? how do the y-coordinates of the vertices change? what type of reflection is the image δabc? how do the x-coordinates of the vertices change? a. the x-coordinates of the vertices are unchanged in the image b. the x-coordinates of the vertices are the same distance away from the y-axis but in the opposite direction. c. the x-coordinates of the vertices are the same distance away from the x-axis but in the opposite direction. d. the x-coordinates of the vertices change differently depending on where they are on the figure

Explanation:

To determine how the x - coordinates of the vertices change when $\triangle ABC$ is reflected to $\triangle A'B'C'$, we analyze the reflection over the y - axis. When a figure is reflected over the y - axis, the rule for the transformation of a point $(x,y)$ is $(x,y)\to(-x,y)$. This means that the x - coordinate of each vertex is multiplied by - 1, so the x - coordinates of the vertices are the same distance away from the y - axis but in the opposite direction.

• Option A is incorrect because the x - coordinates do change (they are negated) during a reflection over the y - axis.
• Option C is incorrect because the description in option C refers to a reflection over the x - axis (which affects y - coordinates), not the x - coordinates in the context of a y - axis reflection.
• Option D is incorrect because in a reflection over the y - axis, the change in x - coordinates follows a consistent rule (multiplying by - 1) and does not depend on the position of the vertex on the figure.

Answer:

B. The x - coordinates of the vertices are the same distance away from the y - axis but in the opposite direction.