Question

1. select all that apply: lines of reflection $y = x$ $y = -x$ $y = k$, k is a constant $x = k$, k is a constant

Explanation:

Step1: Recall the concept of lines of reflection

A line of reflection is a line such that if a figure is reflected over it, the image coincides with the pre - image.

Step2: Analyze \(y = x\)

For any point \((a,b)\) reflected over the line \(y=x\), the image is \((b,a)\). Many symmetric figures (e.g., some polygons) can be reflected over \(y = x\)

Step3: Analyze \(y=-x\)

For a point \((a,b)\) reflected over the line \(y =-x\), the image is \((-b,-a)\). Some symmetric figures can be reflected over \(y=-x\)

Step4: Analyze \(y = k\) (horizontal line)

For a point \((a,b)\) reflected over the line \(y=k\), the image is \((a,2k - b)\). Many symmetric figures (e.g., some polygons with horizontal symmetry) can be reflected over \(y = k\)

Step5: Analyze \(x = k\) (vertical line)

For a point \((a,b)\) reflected over the line \(x=k\), the image is \((2k - a,b)\). Many symmetric figures (e.g., some polygons with vertical symmetry) can be reflected over \(x = k\)

Answer:

All options ( \(y = x\), \(y=-x\), \(y = k\) (where \(k\) is a constant), \(x = k\) (where \(k\) is a constant)) are lines of reflection for some geometric figures. So the answer is \(y = x\), \(y=-x\), \(y = k\) ( \(k\) is a constant), \(x = k\) ( \(k\) is a constant)