can you please help me with this problem

Question

12. Draw a figure on a coordinate plane. Rotate the figure counterclockwise

270° about the origin. How does your drawing confirm your conjecture

in Item 11?

 

The ordered pairs show (x,y) → (  ,   )

Blank 1: 

Blank 2: 

Answer 1

Rotating 270 degrees is the same as rotating 90 degrees in a clockwise direction. For every 90 degrees you rotate, the absolute values of x and y switch. Then we determine which quadrant we are in and apply the appropriate signs to x and y. For this problem our point is (x, y) so we don't know which quadrant we are in. Let's first assume we are in the 1st quadrant. So x and y are positive. Rotating 90 degrees clockwise puts us in the 4th quadrant so our point would be (y, -x). Let's see if that works going from the 2nd quadrant to the 1st quadrant. In the 2nd quadrant x is negative and y is positive. So after rotating 90 degrees clockwise we should get (y, -(-x)) which would be (y, x). This works for the 1st quadrant where x and y are both positive. So we can say that rotating 270 degrees counterclockwise will change point (x, y) to point (y, -x).