Question

in exercises 7, 9, and 11, graph $\triangle jkl$ and its image after a reflection in the given line.7) $j(2,-4), k(3,7), l(6,-1)$; $x$-axis9) $j(2,-1), k(4,-5), l(3,1)$; $x = -1$11) $j(2,4), k(-4,-2), l(-1,0)$; $y = 1$

Explanation:

Step1: Reflect over x-axis (Q7)

Rule: $(x,y)\to(x,-y)$
$J(2,-4)\to J'(2,4)$, $K(3,7)\to K'(3,-7)$, $L(6,-1)\to L'(6,1)$

Step2: Reflect over $x=-1$ (Q9)

Rule: $(x,y)\to(-2-x,y)$
$J(2,-1)\to J'(-4,-1)$, $K(4,-5)\to K'(-6,-5)$, $L(3,1)\to L'(-5,1)$

Step3: Reflect over $y=1$ (Q11)

Rule: $(x,y)\to(x,2-y)$
$J(2,4)\to J'(2,-2)$, $K(-4,-2)\to K'(-4,4)$, $L(-1,0)\to L'(-1,2)$

Answer:

1. For $\triangle JKL$ with $J(2,-4), K(3,7), L(6,-1)$ reflected over the x-axis:

Image vertices: $J'(2,4)$, $K'(3,-7)$, $L'(6,1)$

1. For $\triangle JKL$ with $J(2,-1), K(4,-5), L(3,1)$ reflected over $x=-1$:

Image vertices: $J'(-4,-1)$, $K'(-6,-5)$, $L'(-5,1)$

1. For $\triangle JKL$ with $J(2,4), K(-4,-2), L(-1,0)$ reflected over $y=1$:

Image vertices: $J'(2,-2)$, $K'(-4,4)$, $L'(-1,2)$

(To graph: Plot the original triangle vertices, connect them, then plot the image vertices and connect those to form the reflected triangle on the provided grids.)