Question

a line segment has endpoints at (3, 2) and (2, -3). which reflection will produce an image with endpoints at (3, -2) and (2, 3)?
o 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 rule across the x - axis

When a point \((x,y)\) is reflected across the \(x\) - axis, the transformation rule is \((x,y)\to(x, - y)\).
For the point \((3,2)\), applying the rule \((x,y)\to(x, - y)\) gives \((3,-2)\).
For the point \((2,-3)\), applying the rule \((x,y)\to(x, - y)\) gives \((2,3)\).

Step2: Check other reflection rules

• Reflection across the \(y\) - axis: The rule is \((x,y)\to(-x,y)\). For \((3,2)\) it would be \((-3,2)\) and for \((2,-3)\) it would be \((-2,-3)\), which is not what we want.
• Reflection across the line \(y = x\): The rule is \((x,y)\to(y,x)\). For \((3,2)\) it would be \((2,3)\) and for \((2,-3)\) it would be \((-3,2)\), which is not what we want.
• Reflection across the line \(y=-x\): The rule is \((x,y)\to(-y,-x)\). For \((3,2)\) it would be \((-2,-3)\) and for \((2,-3)\) it would be \((3,-2)\), which is not what we want.

Answer:

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