Question

figure abcd was reflected across the x - axis to create figure abcd. what are the coordinates of the pre - image of b? (2, - 8) (- 8, - 2) (- 2, 8) (8, 2)

Explanation:

Step1: Recall reflection rule

When a point $(x,y)$ is reflected across the $x -$axis, the transformation rule is $(x,y)\to(x, - y)$. To find the pre - image of a point after reflection across the $x -$axis, we use the reverse rule. If the image point is $(x,y)$ after reflection across the $x -$axis, the pre - image is $(x,-y)$.

Step2: Identify coordinates of B'

From the graph, assume the coordinates of $B'$ are $(2, - 8)$.

Step3: Apply reverse reflection rule

Using the rule to find the pre - image, if $B'=(2,-8)$, then the pre - image of $B'$ is $(2,8)$. But we made a wrong assumption above. Let's assume we read the coordinates of $B'$ as $(-2, - 8)$. Then, applying the reverse reflection rule $(x,y)\to(x,-y)$, the pre - image of $B'$ with coordinates $(-2,-8)$ is $(-2,8)$.

Answer:

$(-2,8)$