Question

determine whether the coordinate plane shows a reflection in the x-axis, y-axis, or neither.
3
x - axis
y - axis
neither

Explanation:

Step1: Recall reflection rules

• Reflection over \(x\) - axis: \((x,y)\to(x, - y)\)
• Reflection over \(y\) - axis: \((x,y)\to(-x,y)\)

Step2: Check for \(x\) - axis reflection

Take a point, say if we assume a point \(P(x,y)\) on the blue figure. For \(x\) - axis reflection, the \(y\) - coordinate changes sign. But looking at the figures, this is not the case.

Step3: Check for \(y\) - axis reflection

Take a point \(A\) (for example, assume coordinates of a vertex of the blue figure as \((- 2,-5)\) and a vertex of the red figure as \((2,-5)\)). If \((x,y)=(-2,-5)\), then \((-x,y)=(2,-5)\). This follows the rule \((x,y)\to(-x,y)\) which is the rule for reflection over the \(y\) - axis.

Answer:

\(y\) - axis