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 \(A(3,1)\). If reflected over \(x\) - axis, it would be \((3, - 1)\), but no such point in the red triangle.

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

Take \(A(3,1)\). If reflected over \(y\) - axis, it would be \((-3,1)\). Take \(B(1,1)\) in blue triangle, reflected over \(y\) - axis is \((-1,1)\). Take \(C(2,4)\) in blue triangle, reflected over \(y\) - axis is \((-2,4)\). But in red triangle, points like \(D(-1,-2)\), \(E(-2,-1)\), \(F(-4,-2)\) do not match \(y\) - axis reflection of blue triangle points.

Answer:

neither