Question

what kind of reflection maps the point (4,2) to (4,-2)?
a reflection over the line y = x
b reflection over the x - axis
c reflection over the line y = -x
d reflection over the y - axis

Explanation:

To determine the reflection that maps the point \((4, 2)\) to \((4, -2)\), we analyze the changes in the coordinates:

• The \(x\)-coordinate remains the same (\(4\) in both points).
• The \(y\)-coordinate changes from \(2\) to \(-2\), which is the negative of the original \(y\)-coordinate.

The rule for reflection over the \(x\)-axis is \((x, y) \to (x, -y)\). Applying this rule to \((4, 2)\) gives \((4, -2)\), which matches the transformation.

For the other options:

• Reflection over \(y = x\) would map \((4, 2)\) to \((2, 4)\), not \((4, -2)\).
• Reflection over \(y=-x\) would map \((4, 2)\) to \((-2, -4)\), not \((4, -2)\).
• Reflection over the \(y\)-axis would map \((4, 2)\) to \((-4, 2)\), not \((4, -2)\).

Answer:

b. Reflection over the x - axis