Question

consider reflections of δjkl. what line of reflection maps point k to point k at (-5, 2)? x - axis what line of reflection maps point l to point l at (-2, 3)? x - axis y - axis y = x y = -x j(-3, 9) l(-3, 2) k(5, 2)

Explanation:

Step1: Recall reflection rules

For reflection over the x - axis, the transformation is $(x,y)\to(x, - y)$. For reflection over the y - axis, the transformation is $(x,y)\to(-x,y)$. For reflection over $y = x$, the transformation is $(x,y)\to(y,x)$. For reflection over $y=-x$, the transformation is $(x,y)\to(-y,-x)$.

Step2: Analyze the coordinates of L and L'

Given $L(-3,2)$ and $L'(-2,3)$.
If we consider reflection over $y = x$, applying the rule $(x,y)\to(y,x)$ to $L(-3,2)$ gives $(2,-3)$ which is incorrect.
If we consider reflection over $y=-x$, applying the rule $(x,y)\to(-y,-x)$ to $L(-3,2)$ gives $(-2,3)$ which is correct.
If we consider reflection over the x - axis, applying the rule $(x,y)\to(x, - y)$ to $L(-3,2)$ gives $(-3,-2)$ which is incorrect.
If we consider reflection over the y - axis, applying the rule $(x,y)\to(-x,y)$ to $L(-3,2)$ gives $(3,2)$ which is incorrect.

Answer:

$y = -x$