Question

what is a reflection rule that maps each triangle and its image? the reflection rule is $r_t(x,y)=square$, where the equation of line t is $square$ (simplify your answers.)

Explanation:

Step1: Identify the line of reflection

By observing the graph, the line of reflection \(t\) has a slope of \(1\) and passes through the origin \((0,0)\). The equation of a line in slope - intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For a line with \(m = 1\) and \(b=0\), the equation of line \(t\) is \(y=x\).

Step2: Determine the reflection rule

The rule for reflecting a point \((x,y)\) over the line \(y = x\) is \((x,y)\to(y,x)\). So \(r_t(x,y)=(y,x)\).

Answer:

The reflection rule is \(r_t(x,y)=(y,x)\), where the equation of line \(t\) is \(y = x\)