Question

graph the image of rectangle klmn after a reflection over the x - axis.

Explanation:

Step1: Recall reflection rule

The rule for reflecting a point $(x,y)$ over the $x -$axis is $(x,-y)$.

Step2: Find new coordinates of vertices

Let's assume the coordinates of the vertices of rectangle $KLMN$ are $K(x_1,y_1)$, $L(x_2,y_2)$, $M(x_3,y_3)$, $N(x_4,y_4)$. After reflection over the $x -$axis, the new coordinates will be $K'(x_1,-y_1)$, $L'(x_2,-y_2)$, $M'(x_3,-y_3)$, $N'(x_4,-y_4)$. For example, if $K = (- 4,-4)$, then $K'=(-4,4)$; if $L=(6,-4)$, then $L'=(6,4)$; if $M=(6,-2)$, then $M'=(6,2)$; if $N=(-4,-2)$, then $N'=(-4,2)$.

Step3: Plot new rectangle

Plot the points $K'$, $L'$, $M'$, $N'$ on the coordinate - plane and connect them in order to form the new rectangle.

Answer:

Plot the points obtained by changing the sign of the $y -$coordinates of the vertices of rectangle $KLMN$ and connect them to form the reflected rectangle.