Question

reasoning one image of $\triangle abc$ is $\triangle abc$. 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 $\triangle abc$?
the x - coordinates of the vertices change differently depending on where they are on the figure
how do the y - coordinates of the vertices change?
a. the y - coordinates of the vertices are unchanged in the image.
b. the y - coordinates of the vertices are the same distance away from the y - axis but in the opposite direction
c. the y - coordinates of the vertices change differently depending on where they are on the figure
d. the y - coordinates of the vertices are the same distance away from the x - axis but in the opposite direction
what type of reflection is the image $\triangle abc$?
a. $\triangle abc$ is the image of $\triangle abc$ after a reflection across the line $x = - 2$
b. $\triangle abc$ is the image of $\triangle abc$ after a reflection across the y - axis
c. $\triangle abc$ is the image of $\triangle abc$ after a reflection across the x - axis
d. $\triangle abc$ is the image of $\triangle abc$ after a reflection across the line $y = - 2$

Explanation:

How do the y - coordinates of the vertices change?

When a figure is reflected across the y - axis (which is the case here as we will see later), the y - coordinates of the vertices remain the same. Let's analyze the options:

• Option B is incorrect because y - coordinates do not change based on position in a reflection over y - axis.
• Option C is incorrect as y - coordinates are not related to distance from y - axis in terms of changing direction (that's for x - coordinates in y - axis reflection).
• Option D is incorrect as it describes reflection over x - axis (where y - coordinates change sign), but here we have reflection over y - axis.
• Option A is correct because in a reflection across the y - axis, the y - coordinates of the vertices are unchanged.

• Option A: A reflection across $x=-2$ would not result in the symmetric figure about y - axis as seen.
• Option B: When we reflect a figure across the y - axis, the x - coordinates of the vertices change sign (or are at the same distance from y - axis on the opposite side) and y - coordinates remain the same. This matches the transformation of $\triangle ABC$ to $\triangle A'B'C'$ as seen from the graph.
• Option C: A reflection across x - axis would change the sign of y - coordinates, which is not the case here.
• Option D: A reflection across $y = - 2$ would change the y - coordinates, which is not what we observe.

Answer:

A. The y - coordinates of the vertices are unchanged in the image.

What type of reflection is the image $\triangle A'B'C'$?