Question

xyz with vertices x(1, 1), y(3, 5), and z(5, 1) will be rotated 180° about the origin. what will be the coordinates of y?

1. (-5, 3)
2. (-2, -5)
3. (5, -5)
4. (5, 3)

Explanation:

Step1: Recall rotation rule

The rule for rotating a point $(x,y)$ 180° about the origin is $(x,y)\to(-x,-y)$.

Step2: Identify coordinates of Y

The coordinates of Y are $(3,5)$.

Step3: Apply rotation rule

For point Y with $x = 3$ and $y = 5$, after rotation, $x'=-3$ and $y'=-5$. So the new - coordinates of Y are $(-3,-5)$.

Answer:

$(-3,-5)$