Question

consider reflections of δjkl. 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

For a point $(x,y)$ reflected over the $y -$axis, the new point is $(-x,y)$. For reflection over the $x -$axis, the new point is $(x, - y)$. For reflection over $y = x$, the new point is $(y,x)$ and for reflection over $y=-x$, the new point is $(-y,-x)$.

Step2: Analyze reflection of point K

Point $K(5,2)$ is mapped to $K'(-5,2)$. The $y -$coordinate remains the same and the $x -$coordinate changes its sign. This follows the rule of reflection over the $y -$axis.

Step3: Analyze reflection of point L

Point $L(-3,2)$ is mapped to $L'(-2,3)$.
Let's check each reflection rule:

• Reflection over $x -$axis: $(-3,2)\to(-3,-2)$, not correct.
• Reflection over $y -$axis: $(-3,2)\to(3,2)$, not correct.
• Reflection over $y = x$: $(-3,2)\to(2,-3)$, not correct.
• Reflection over $y=-x$: $(-3,2)\to(-2,3)$. This is correct.

Answer:

The line of reflection that maps point $K$ to $K'$ is the $y -$axis. The line of reflection that maps point $L$ to $L'$ is $y=-x$.