Question

what line of reflection will give an image with point b at (-4,2)? x=-3 y=-2 y=x y=-x

Explanation:

Step1: Recall reflection rules

For a point \((x,y)\) reflected over \(y = -x\), the transformation is \((x,y)\to(-y,-x)\). Given point \(B'(-4,2)\), if we reflect it over \(y=-x\), the image point \(B\) has coordinates \((-2,4)\).

Step2: Check other lines

• For reflection over \(x = - 3\), the \(y\)-coordinate remains the same and the \(x\)-coordinate changes based on the distance from \(x=-3\). It won't give the correct transformation for \(B'\) to its pre - image.
• For reflection over \(y=-2\), the \(x\)-coordinate remains the same and the \(y\)-coordinate changes based on the distance from \(y = - 2\). It won't give the correct transformation.
• For reflection over \(y = x\), the transformation is \((x,y)\to(y,x)\), which is not applicable here as it won't map \(B'(-4,2)\) to its pre - image.

Answer:

y = -x