Question

triangle abc is reflected across a line to create triangle abc.
what is the line of reflection?
$y = -3x$
$y = 2$
$x = 2$
$y = x$
clear my selection

Explanation:

Step1: Analyze the line \(y = - 3x\)

This is a line with a slope of \(-3\). But from the graph, we can see that it is not the line of reflection.

Step2: Analyze the line \(y = 2\)

This is a horizontal line. But from the graph, we can see that it is not the line of reflection.

Step3: Analyze the line \(x = 2\)

This is a vertical line. But from the graph, we can see that it is not the line of reflection.

Step4: Analyze the line \(y=x\)

The line \(y = x\) has a slope of \(1\) and passes through the origin. For a reflection across the line \(y=x\), the \(x\) and \(y\) coordinates of a point \((a,b)\) are swapped to \((b,a)\). From the graph, we can observe that this is the line of reflection.

Answer:

\(y = x\)