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 rule is \((x,y)\to(x, - y)\). So, to find the pre - image (original point before reflection), if the image is \((x',y')\), the pre - image is \((x',-y')\).

Step2: Locate \(B'\)

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

Step3: Apply the inverse of the reflection rule

Using the inverse of the \(x -\)axis reflection rule \((x,y)\to(x, - y)\) (i.e., to get the pre - image from the image, we use \((x,y)\to(x,-y)\) in reverse: if image is \((x,y)\), pre - image is \((x,-y)\)). For \(B'(-2,-8)\), the pre - image \(B\) has coordinates \((-2,8)\) since \(-(-8)=8\).

Answer:

C. (-2, 8)