Question

fluency and skills practice name: lesson 2 • session 3 performing a rotation in the coordinate plane continued ① the table shows how the coordinates change when you rotate a point 270° clockwise around the origin. original a(6, 2) b(8, - 4) c(-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° counter - clockwise around the origin? ② how is the image that results from a 90° counter - clockwise rotation similar to the image that results from a 270° clockwise rotation? how is it different?

Explanation:

Step1: Recall rotation rules

A 270 - degree counter - clockwise rotation around the origin is equivalent to a 90 - degree clockwise rotation. The general rule for a 90 - degree clockwise rotation of a point \((x,y)\) around the origin is \((y,-x)\).

Step2: Analyze similarity and difference

For a 90 - degree counter - clockwise rotation of a point \((x,y)\), the rule is \((-y,x)\). For a 270 - degree clockwise rotation of a point \((x,y)\), the rule is also \((-y,x)\). So, the similarity is that for a point \((x,y)\), the coordinates of the image after a 90 - degree counter - clockwise rotation and a 270 - degree clockwise rotation are the same. The difference is in the direction of rotation. One is in the counter - clockwise direction and the other is in the clockwise direction.

Answer:

1. The coordinates of the image of a point \((x,y)\) rotated 270° counter - clockwise around the origin are \((y,-x)\).
2. Similarity: The coordinates of the image of a point \((x,y)\) are the same for a 90° counter - clockwise rotation and a 270° clockwise rotation. Difference: The directions of rotation are different; one is counter - clockwise and the other is clockwise.