Question

luis is programming an animation for a countdown timer where points flash in sequence, one at a time, around in a circle. he calculates that the coordinates of the first four points in his sequence are (6,0), (5.5,2.3),(4.2,4.2), and (2.3,5.5). he can find the rest of the coordinates by rotating the first four points 90°, 180°, and 270°. what are the coordinates that complete the sequence around in a circle? when rotated 90°, the points are (type ordered - pairs. use a comma to separate answers as needed.)

Explanation:

Step1: Recall rotation rule for 90 - degree counter - clockwise

For a point $(x,y)$ rotated 90 - degree counter - clockwise about the origin, the new point is $(-y,x)$.

Step2: Rotate point $(6,0)$

For $(x = 6,y = 0)$, new point is $(-0,6)=(0,6)$.

Step3: Rotate point $(5.5,2.3)$

For $x = 5.5,y = 2.3$, new point is $(-2.3,5.5)$.

Step4: Rotate point $(4.2,4.2)$

For $x = 4.2,y = 4.2$, new point is $(-4.2,4.2)$.

Step5: Rotate point $(2.3,5.5)$

For $x = 2.3,y = 5.5$, new point is $(-5.5,2.3)$.

Answer:

$(0,6),(-2.3,5.5),(-4.2,4.2),(-5.5,2.3)$