Question

performing a rotation in the coordinate plane continued
13 the table shows how the coordinates change when you rotate a point 270° clockwise around the origin.

original	(6, 2)	(8, -4)	(-1, 9)
rotated 270° clockwise	(-2, 6)	(4, 8)	(-9, -1)

what are the coordinates of the image of a point (x, y) that is rotated 270° counterclockwise around the origin?

Explanation:

Step1: Recall rotation rules

A $270^{\circ}$ counter - clockwise rotation is the same as a $90^{\circ}$ clockwise rotation. The general rule for a $90^{\circ}$ clockwise rotation of a point $(x,y)$ about the origin is $(x,y)\to(y, - x)$.

Step2: Apply the rule

For a point $(x,y)$ rotated $270^{\circ}$ counter - clockwise (or $90^{\circ}$ clockwise) around the origin, the new coordinates are $(y,-x)$.

Answer:

$(y, - x)$