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 the 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 the rules to the endpoints

• For the point \((-4,-6)\):
• If we reflect across the \(y\) - axis, using the rule \((x,y)\to(-x,y)\), we get \((-(-4),-6)=(4,-6)\)
• For the point \((-6,4)\):
• If we reflect across the \(y\) - axis, using the rule \((x,y)\to(-x,y)\), we get \((-(-6),4)=(6,4)\)

Since reflecting the endpoints \((-4,-6)\) and \((-6,4)\) across the \(y\) - axis gives us the endpoints \((4,-6)\) and \((6,4)\), the correct answer is a reflection of the line segment across the \(y\) - axis.

Answer:

B. a reflection of the line segment across the y - axis