Question

lesson 2 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? (y, -x) 14 how is the image that results from a 90° counterclockwise rotation similar to the image that results from a 270° clockwise rotation? how is it different?

Explanation:

Step1: Recall rotation rules

A $90^{\circ}$ counter - clockwise rotation of a point $(x,y)$ about the origin has the transformation rule $(x,y)\to(-y,x)$. A $270^{\circ}$ clockwise rotation of a point $(x,y)$ about the origin also has the transformation rule $(x,y)\to(-y,x)$.

Step2: Analyze similarities

The similarity is that for a point $(x,y)$ in the coordinate - plane, both a $90^{\circ}$ counter - clockwise rotation and a $270^{\circ}$ clockwise rotation about the origin result in the same transformation of coordinates. The new coordinates of the point $(x,y)$ are $(-y,x)$ for both rotations.

Step3: Analyze differences

The difference is in the direction of rotation. One is a $90^{\circ}$ turn in the counter - clockwise direction and the other is a $270^{\circ}$ turn in the clockwise direction.

Answer:

Similarity: They result in the same coordinate transformation for a point $(x,y)$ (the new coordinates are $(-y,x)$).
Difference: The directions of rotation are different; one is $90^{\circ}$ counter - clockwise and the other is $270^{\circ}$ clockwise.