Question

when reflecting over the x - axis...
keep the y - value the same, and maintain
the same number of units away from the
line for the x - value.
change the sign of the y - values.
change the sign of the x - values.
keep the x - value the same, and maintain
the same number of units away from the
line for the y - value.

Explanation:

Step1: Recall reflection over x - axis rule

When reflecting a point \((x,y)\) over the \(x\) - axis, the \(x\) - coordinate remains the same, and the \(y\) - coordinate changes its sign. Mathematically, the transformation is \((x,y)\to(x, - y)\).

Step2: Analyze each option

• Orange option: Incorrect. When reflecting over the \(x\) - axis, the \(y\) - value changes sign, not remains the same.
• Blue option: Correct. Since \((x,y)\to(x, - y)\), we change the sign of the \(y\) - values.
• Green option: Incorrect. Changing the sign of the \(x\) - values is the rule for reflection over the \(y\) - axis (\((x,y)\to(-x,y)\)).
• Red option: Incorrect. When reflecting over the \(x\) - axis, we focus on changing the \(y\) - value's sign while keeping \(x\) the same, not maintaining units for \(y\) in the way described.

Answer:

Blue option: Change the sign of the \(y\) - values.