Question

a. use your new knowledge about rotations to design a pattern for a pinwheel. start with the triangle shown in the diagram in quadrant i. rotate the triangle counter - clockwise by 90°, 180°, and 270° about the origin. write the coordinates of the vertices of each of the three rotated triangles in the pattern.

Explanation:

Step1: Recall 90 - degree counter - clockwise rotation rule

For a point $(x,y)$ rotated 90 - degree counter - clockwise about the origin, the new coordinates are $(-y,x)$.
For the points $(0,0)$, $(3,0)$ and $(3,5)$:

• For $(0,0)$: $(-0,0)=(0,0)$
• For $(3,0)$: $(0,3)$
• For $(3,5)$: $(-5,3)$

Step2: Recall 180 - degree counter - clockwise rotation rule

For a point $(x,y)$ rotated 180 - degree counter - clockwise about the origin, the new coordinates are $(-x,-y)$.

• For $(0,0)$: $(0,0)$
• For $(3,0)$: $(-3,0)$
• For $(3,5)$: $(-3,-5)$

Step3: Recall 270 - degree counter - clockwise rotation rule

For a point $(x,y)$ rotated 270 - degree counter - clockwise about the origin, the new coordinates are $(y, - x)$.

• For $(0,0)$: $(0,0)$
• For $(3,0)$: $(0,-3)$
• For $(3,5)$: $(5,-3)$

Answer:

90 - degree rotation: $(0,0),(0,3),(-5,3)$
180 - degree rotation: $(0,0),(-3,0),(-3,-5)$
270 - degree rotation: $(0,0),(0,-3),(5,-3)$