Question

which image shows the preimage reflected over the x - axis?
options:
image b
image a
none of these
image c

Explanation:

Step1: Recall reflection over x - axis rule

The rule for reflecting a point \((x,y)\) over the \(x\) - axis is \((x,y)\to(x, - y)\). Let's assume the pre - image point has coordinates \((x,y)\). After reflection over the \(x\) - axis, the \(x\) - coordinate remains the same and the \(y\) - coordinate changes its sign.

Step2: Analyze each image

• For Image B: If the pre - image point is, say, \((a,b)\), after reflection over \(x\) - axis, the point should be \((a, - b)\). Looking at the graph of Image B, it seems to follow the rule of reflection over the \(x\) - axis (the \(x\) - coordinate is the same as the pre - image and the \(y\) - coordinate is the negative of the pre - image's \(y\) - coordinate).
• For Image A: The transformation here does not seem to be a reflection over the \(x\) - axis (the change in coordinates does not match the \((x,y)\to(x, - y)\) rule).
• For Image C: The transformation here does not seem to be a reflection over the \(x\) - axis (the change in coordinates does not match the \((x,y)\to(x, - y)\) rule).

Answer:

Image B