Question

graph the image of square klmn after a reflection over the line y = -1.

Explanation:

Step1: Recall reflection rule for y - coordinate

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 reflected points

Let's assume $K(-2,1)$, $L(2,1)$, $M(2,5)$, $N(-2,5)$.
For point $K(-2,1)$:
$x'=-2$, $y'=2\times(-1)-1=-2 - 1=-3$. So $K'(-2,-3)$.
For point $L(2,1)$:
$x' = 2$, $y'=2\times(-1)-1=-3$. So $L'(2,-3)$.
For point $M(2,5)$:
$x'=2$, $y'=2\times(-1)-5=-2 - 5=-7$. So $M'(2,-7)$.
For point $N(-2,5)$:
$x'=-2$, $y'=2\times(-1)-5=-7$. So $N'(-2,-7)$.

Step3: Graph the new square

Plot the points $K'(-2,-3)$, $L'(2,-3)$, $M'(2,-7)$, $N'(-2,-7)$ and connect them to form the reflected square.

Answer:

Graph the square with vertices $K'(-2,-3)$, $L'(2,-3)$, $M'(2,-7)$, $N'(-2,-7)$ on the given coordinate - plane.