Question

1. d(3, 5) is the image of d after a 270° counterclockwise rotation about the origin. what are the coordinates of d?

Explanation:

Step1: Recall rotation rule

The rule for a $270^{\circ}$ counter - clockwise rotation about the origin is $(x,y)\to(y, - x)$. Let the coordinates of $D$ be $(x,y)$. After rotation, $D(x,y)$ becomes $D'(y,-x)$.

Step2: Set up equations

We know that $D'(3,5)$ and $D'(y, - x)$. So we have the equations $y = 3$ and $-x=5$.

Step3: Solve for $x$ and $y$

From $-x = 5$, we get $x=-5$. And we already have $y = 3$.

Answer:

$(-5,3)$