Question

triangle lmn is reflected across a line, ( l=(12, -7) ), and ( l=(-7, 12) ). what is the line of reflection? the ( x )-axis the line ( y = x ) the line ( y=-x ) the ( y )-axis

Explanation:

Step1: Recall reflection rules

For a point \((x,y)\) reflected over the \(x\) - axis, the image is \((x, - y)\). For a point \((x,y)\) reflected over the \(y\) - axis, the image is \((-x,y)\). For a point \((x,y)\) reflected over the line \(y = x\), the image is \((y,x)\). For a point \((x,y)\) reflected over the line \(y=-x\), the image is \((-y,-x)\).

Step2: Apply the rules to the given points

Given \(L=(12,-7)\) and \(L'=(-7,12)\).
If we consider the rule for reflection over the line \(y = x\), when \(x = 12\) and \(y=-7\), the image of the point \((x,y)\) under reflection over \(y = x\) is \((y,x)\). Substituting \(x = 12\) and \(y=-7\) into the rule \((y,x)\), we get \((-7,12)\) which is \(L'\).

Answer:

the line \(y = x\)