Question

a line segment has endpoints at $(-4, -6)$ and $(-6, 4)$. which reflection will produce an image with endpoints at $(4, -6)$ and $(6, -4)$?

• a reflection of the line segment across the $x$-axis
• a reflection of the line segment across the $y$-axis
• a reflection of the line segment across the line $y = x$
• a reflection of the line segment across the line $y = -x$

Explanation:

Step1: Recall reflection rules

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

Step2: Apply reflection rules to endpoints

• For the point \((-4,-6)\):
• Reflection across \(y -\)axis: \((-4,-6)\to(4,-6)\)
• For the point \((-6,4)\):
• Reflection across \(y -\)axis: \((-6,4)\to(6,4)\)

Answer:

a reflection of the line segment across the \(y -\)axis