Question

give the coordinates of the new image.

1. trapezoid jklm with vertices j(-4, 3), k(-2, 7), l(2, 7), and m(3, 3): y = 1

j ( )
k ( )
l ( )
m ( )

Explanation:

Step1: Recall reflection formula

For a point $(x,y)$ reflected over the line $y = a$, the new - y - coordinate is $y'=2a - y$ and the x - coordinate remains the same, i.e., $x'=x$. Here $a = 1$.

Step2: Find coordinates of $J'$

For point $J(-4,3)$, $x=-4$ and $y = 3$. Using the formula $y'=2\times1 - 3=-1$ and $x'=-4$. So $J'(-4,-1)$.

Step3: Find coordinates of $K'$

For point $K(-2,7)$, $x=-2$ and $y = 7$. Using the formula $y'=2\times1 - 7=-5$ and $x'=-2$. So $K'(-2,-5)$.

Step4: Find coordinates of $L'$

For point $L(2,7)$, $x = 2$ and $y = 7$. Using the formula $y'=2\times1 - 7=-5$ and $x'=2$. So $L'(2,-5)$.

Step5: Find coordinates of $M'$

For point $M(3,3)$, $x = 3$ and $y = 3$. Using the formula $y'=2\times1 - 3=-1$ and $x'=3$. So $M'(3,-1)$.

Answer:

$J'(-4,-1)$
$K'(-2,-5)$
$L'(2,-5)$
$M'(3,-1)$