Question

1. the graph of trapezoid abcd is shown. graph the image of abcd after a reflection across the x - axis. write the coordinates of the reflected image.

Explanation:

Step1: Recall reflection rule

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

Step2: Assume coordinates

Suppose the coordinates of trapezoid $ABCD$ are $A(x_1,y_1)$, $B(x_2,y_2)$, $C(x_3,y_3)$, $D(x_4,y_4)$.

Step3: Find reflected - coordinates

The reflected coordinates will be $A'(x_1, - y_1)$, $B'(x_2,-y_2)$, $C'(x_3,-y_3)$, $D'(x_4,-y_4)$. For example, if $A(-3,-1)$, $B(-4,-3)$, $C(3,-3)$, $D(2,-1)$, then $A'(-3,1)$, $B'(-4,3)$, $C'(3,3)$, $D'(2,1)$. To graph the reflected trapezoid, plot the new points $A'$, $B'$, $C'$, $D'$ and connect them in order.

Answer:

The coordinates of the reflected trapezoid are obtained by changing the sign of the $y -$coordinates of the original trapezoid's vertices. Graph by plotting the new - coordinate points.