Question

what is a reflection rule that maps the triangle and its image? the reflection rule is ( r_{t}(x,y)=) where ( t ) is the line (type an equation.)

Explanation:

Step1: Recall reflection rules

For a reflection over the line \(y = -x\), the rule is \(r_{y=-x}(x,y)=( - y,-x)\).

Step2: Verify with points

Take a point, say \(R(1,0)\). After reflection, \(R'\) should be \((0, - 1)\). Using the rule \(r_{y=-x}(1,0)=(0,-1)\). Another point \(Q(1,-1)\), \(r_{y = - x}(1,-1)=(1,-1)\) (incorrect, wait, no, take \(P(-2,3)\). Using \(r_{y=-x}(x,y)=(-y,-x)\), \(r_{y=-x}(-2,3)=(-3,2)\). Looking at the graph, if the line of reflection is \(y=-x\) (since the blue - dashed line has a slope of \(- 1\) and passes through the origin (\(y=-x\) has the form \(y = mx + b\) with \(m=-1\) and \(b = 0\))).

Answer:

The reflection rule is \(r_{t}(x,y)=(-y,-x)\) where \(t\) is the line \(y=-x\).