Question

1. write a rule for each counterclockwise rotation about the origin: 90°: (x,y)→____ 180°: (x,y)→__ 270°: (x,y)→____

Explanation:

Step1: Recall 90 - degree rotation rule

For a 90 - degree counter - clockwise rotation about the origin, the rule is to swap the x and y coordinates and change the sign of the new x - coordinate. So, $(x,y)\to(-y,x)$.

Step2: Recall 180 - degree rotation rule

For a 180 - degree counter - clockwise rotation about the origin, we change the sign of both the x and y coordinates. So, $(x,y)\to(-x,-y)$.

Step3: Recall 270 - degree rotation rule

For a 270 - degree counter - clockwise rotation about the origin, it is equivalent to a 90 - degree clockwise rotation. We swap the x and y coordinates and change the sign of the new y - coordinate. So, $(x,y)\to(y, - x)$.

Answer:

$90^{\circ}:(x,y)\to(-y,x)$
$180^{\circ}:(x,y)\to(-x,-y)$
$270^{\circ}:(x,y)\to(y,-x)$