Question

write a rule to describe the transformation below. answer attempt 5 out of 6 rotation about the origin

Explanation:

Step1: Analyze the transformation

To find the rule for the transformation, we can use the properties of rotation. For a rotation of \(180^{\circ}\) about the origin, the general rule for a point \((x,y)\) is \((x,y)\to(-x,-y)\).

Let's take a point from the original figure. Suppose we have a point \(W\) (let's assume its coordinates for illustration purposes. If \(W=(x_1,y_1)\) in the original figure and its image \(W'\) has coordinates \((-x_1,-y_1)\) after rotation.

We can also check other points. For example, if we consider a point \(S\) with coordinates \((x_2,y_2)\) in the original figure, after a \(180^{\circ}\) rotation about the origin, its image \(S'\) will have coordinates \((-x_2,-y_2)\)

Answer:

The rule for the transformation is a rotation of \(180^{\circ}\) about the origin. The general rule for a point \((x,y)\) is \((x,y)\to(-x,-y)\)