Question

reflecting a triangle
consider reflections of △jkl.
what line of reflection maps point k to point k at (-5, 2)?
y - axis
what line of reflection maps point l to point l at (-2, 3)?
x - axis
y - axis
y = x
y = -x

Explanation:

Step1: Recall reflection rules

Reflection across y - axis changes sign of x - coordinate while y - coordinate remains same. Point K(5, 2) reflected across y - axis gives K'(-5, 2).

Step2: Analyze L and L'

Point L(-3, 2) and L'(-2, 3). Reflection across y = x swaps x and y coordinates. But here, if we consider the transformation, reflection across y = x is not correct. Reflection across x - axis changes sign of y - coordinate. Here, this is not relevant. Reflection across y - axis changes sign of x - coordinate. For L(-3, 2), reflection across y - axis gives (3, 2) which is not L'. Let's consider the mid - point between L(-3, 2) and L'(-2, 3). The line y=-x has the transformation rule (x,y)→(-y,-x). But this is not correct either. By observing the coordinates, we note that the transformation from L(-3, 2) to L'(-2, 3) is not a simple reflection among the given options. However, if we consider the general rules, for a point (x,y) reflected across y = x, the new point is (y,x). But the coordinates don't match exactly for a simple reflection. If we assume there is an error in the problem setup and we focus on the common reflection rules, for the first part, reflection of K(5,2) to K'(-5,2) is y - axis reflection. For L(-3,2) to L'(-2,3), if we assume we are looking for a simple reflection among the options and there is some mis - typing or mis - understanding in the coordinates of L', if we were to consider the correct reflection rules for the given options, and assume we want to match the x - coordinate sign change concept similar to the first part, we note that for L(-3,2), reflection across y - axis gives (3,2) which is wrong. Reflection across x - axis changes y - value sign which is wrong. Reflection across y = x swaps x and y which is wrong. Reflection across y=-x gives (-2,3) when we assume some adjustment in the problem context. In a standard sense, for the first part:
The rule for reflecting a point (x,y) across the y - axis is (x,y)→(-x,y). For K(5,2), (5,2)→(-5,2) which is a y - axis reflection.

Answer:

The line of reflection that maps point K to point K' is the y - axis. For point L to point L', among the given options, there seems to be an issue with the problem setup as the transformation from L(-3,2) to L'(-2,3) does not match the standard reflection rules of the given options precisely. But if we were to force a choice based on the common reflection concepts, none of the options are correct for the transformation of L to L' in a strict sense. For K, the answer is y - axis.