Question

transformations quiz
what is the rule used to transform δabc to its image?
a(-3,5), b(2,8), c(-4,-5) and a(-3,-5), b(2,-8), c(-4,5)
reflection over the line y=-2
reflection over the y-axis
reflection over the x-axis
reflection over the line y=x

Explanation:

Step1: Recall reflection rules

For a point \((x,y)\):

• Reflection over \(x\)-axis: \((x,-y)\)
• Reflection over \(y\)-axis: \((-x,y)\)
• Reflection over \(y = x\): \((y,x)\)
• Reflection over \(y=-2\): involves midpoint calculation, but let's check coordinates first.

Step2: Analyze given points

• \(A(-3,5)\) becomes \(A'(-3,-5)\): \(x\) stays same, \(y\) becomes \(-y\)
• \(B(2,8)\) becomes \(B'(2,-8)\): \(x\) stays same, \(y\) becomes \(-y\)
• \(C(-4,-5)\) becomes \(C'(-4,5)\): \(x\) stays same, \(y\) becomes \(-y\)

This matches the rule for reflection over \(x\)-axis: \((x,y)\to(x,-y)\)

Answer:

Reflection over the x - axis