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

Step2: Check coordinates

Assume coordinates (by counting grid units):

• Let’s say \(A=(2,1)\), \(B=(2,3)\), \(C=(6,1)\) for blue triangle.
• For red triangle, if it were reflection over \(x\) - axis, \(A=(2,1)\) would map to \((2, - 1)\), but red - triangle point \(D=(2, - 1)\) (matches \(x\) - coordinate reflection rule for \(A\)).
• \(B=(2,3)\) would map to \((2,-3)\) (red - triangle point \(E=(2, - 3)\) matches).
• \(C=(6,1)\) would map to \((6,-1)\) (red - triangle point \(F=(6, - 1)\) matches)

Answer:

\(x\) - axis