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

Step2: Apply reflection rules to the endpoints

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

Answer:

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