Question

triangle klm and triangle klm are shown on the coordinate plane. write the rule describes the composition of transformations that maps triangle klm to triangle klm. enter your answers in the boxes. r(o,°)∘t(,)(x,y)

Explanation:

Step1: Analyze the x - coordinate change

Let's take a point, say point L(3,6). Its corresponding point L'(3, - 2). The x - coordinate remains the same, i.e., there is no horizontal translation.

Step2: Analyze the y - coordinate change

The y - coordinate of L changes from 6 to - 2. The change in the y - coordinate is \(6-(-2)=8\). The figure is reflected over the x - axis (which changes the sign of the y - coordinate) and then translated down by 2 units. The general rule for reflection over the x - axis is \((x,y)\to(x, - y)\) and then for translation down by 2 units is \((x,-y)\to(x,-y - 2)\). So the composition of transformations is \(R_{x - axis}\circ T_{0,-2}(x,y)=(x,-y - 2)\)

Answer:

\(R_{x - axis}\circ T_{0,-2}(x,y)=(x,-y - 2)\)