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, the coordinates of point $B'$ 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 $B'$ has coordinates $(2,8)$. But there is a mistake above. The correct rule for finding the pre - image of a point $(x,y)$ (image after $x$ - axis reflection) is to change the sign of the $y$ - coordinate. The coordinates of $B'$ from the graph are $(2,-8)$. So the pre - image of $B'$ is $(2,8)$ which is not in the options. Let's re - check. If we assume we read the coordinates wrong and $B'$ is actually $(-2, - 8)$, then the pre - image is $(-2,8)$.

Answer:

C. $(-2,8)$