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 line $y = k$

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

Step2: Find the image of point J

For point $J(3,-5)$, using the formula $(x,2k - y)$ with $x = 3$, $y=-5$ and $k=-3$. We have $2\times(-3)-(-5)=-6 + 5=-1$. So the image of $J$ is $J'(3,-1)$.

Step3: Find the image of point K

For point $K(4,-1)$, using the formula $(x,2k - y)$ with $x = 4$, $y=-1$ and $k=-3$. We have $2\times(-3)-(-1)=-6 + 1=-5$. So the image of $K$ is $K'(4,-5)$.

Step4: Find the image of point L

For point $L(0,-3)$, using the formula $(x,2k - y)$ with $x = 0$, $y=-3$ and $k=-3$. We have $2\times(-3)-(-3)=-6+3=-3$. So the image of $L$ is $L'(0,-3)$.

Step5: Graph the original and reflected polygons

Plot the original points $J(3,-5)$, $K(4,-1)$, $L(0,-3)$ and connect them to form the original polygon. Then plot the reflected - points $J'(3,-1)$, $K'(4,-5)$, $L'(0,-3)$ and connect them to form the reflected polygon.

Answer:

The original polygon has vertices $J(3,-5)$, $K(4,-1)$, $L(0,-3)$. The reflected polygon over the line $y=-3$ has vertices $J'(3,-1)$, $K'(4,-5)$, $L'(0,-3)$. Graph both polygons on the coordinate - plane.