Question

graph the polygon with the given vertices and its image after a reflection in the given line. j(3, - 5), k(4, - 1), l(0, - 3); y = - 3

Explanation:

Step1: Recall reflection rule

For a point $(x,y)$ reflected over the horizontal line $y = k$, the rule is $(x,2k - y)$. Here $k=-3$.

Step2: Reflect point J

For $J(3,-5)$, using the rule $(x,2k - y)$ with $x = 3,k=-3,y=-5$. We get $J'(3,2\times(-3)-(-5))=(3,-6 + 5)=(3,-1)$.

Step3: Reflect point K

For $K(4,-1)$, with $x = 4,k=-3,y=-1$. We have $K'(4,2\times(-3)-(-1))=(4,-6 + 1)=(4,-5)$.

Step4: Reflect point L

For $L(0,-3)$, since $y=-3$ (the line of reflection), $L$ is on the line of reflection, so $L'(0,-3)$.

Answer:

The vertices of the original polygon are $J(3,-5),K(4,-1),L(0,-3)$ and the vertices of the reflected polygon are $J'(3,-1),K'(4,-5),L'(0,-3)$.