Question

graph the polygon with the given vertices and its image after a reflection in the given line. j(1, - 1), k(3,0), l(0, - 4); x = 2

Explanation:

Step1: Recall reflection formula

For a point $(x,y)$ reflected over the line $x = a$, the new - point $(x',y')$ is given by the formula $x'=2a - x$ and $y'=y$. Here $a = 2$.

Step2: Find the image of point J

For point $J(1,-1)$, using the formula $x'=2\times2 - 1=3$ and $y'=-1$. So the image of $J$ is $J'(3,-1)$.

Step3: Find the image of point K

For point $K(3,0)$, using the formula $x'=2\times2 - 3 = 1$ and $y'=0$. So the image of $K$ is $K'(1,0)$.

Step4: Find the image of point L

For point $L(0,-4)$, using the formula $x'=2\times2 - 0=4$ and $y'=-4$. So the image of $L$ is $L'(4,-4)$.

Answer:

The vertices of the original polygon are $J(1,-1)$, $K(3,0)$, $L(0,-4)$. The vertices of the image after reflection over the line $x = 2$ are $J'(3,-1)$, $K'(1,0)$, $L'(4,-4)$. To graph, plot the points $J(1,-1)$, $K(3,0)$, $L(0,-4)$ and connect them to form the original polygon, then plot the points $J'(3,-1)$, $K'(1,0)$, $L'(4,-4)$ and connect them to form the reflected polygon.