Question

the coordinates of a point and its image after a reflection are given. is the reflection in the x - axis or y - axis? explain your reasoning.

1. (0,3)→(0, - 3)
2. (1,5)→( - 1,5)

Explanation:

Step1: Recall reflection rules

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

Step2: Analyze point \((0,3)\to(0, - 3)\)

For the point \((0,3)\) and its image \((0,-3)\), the \(x -\)coordinate remains \(0\) (unchanged), and the \(y -\)coordinate changes sign. According to the rule \((x,y)\to(x, - y)\), this is a reflection in the \(x -\)axis.

Step3: Analyze point \((1,5)\to(-1,5)\)

For the point \((1,5)\) and its image \((-1,5)\), the \(y -\)coordinate remains \(5\) (unchanged), and the \(x -\)coordinate changes sign. According to the rule \((x,y)\to(-x,y)\), this is a reflection in the \(y -\)axis.

Answer:

• For \((0,3)\to(0, - 3)\): reflection in the \(x -\)axis.
• For \((1,5)\to(-1,5)\): reflection in the \(y -\)axis.