Question

determine whether the coordinate plane shows a reflection in the $x$-axis, $y$-axis, or neither
$x$-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 from the blue triangle, say \(B(1,2)\). If reflected over \(x\) - axis, it should be \((1,-2)\), but there is no such point in the red triangle.

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

Take a point from the blue triangle, say \(B(1,2)\). If reflected over \(y\) - axis, it should be \((- 1,2)\), but there is no such point in the red triangle.

Answer:

neither