Question

rotations about a point (non - origin)
whats the process? make your own steps here!

1. subtract the point of rotation from each vertex point of the shape
2. rotate as you would around the origin
3. add the point of rotation back to each vertex point

show work here:

Explanation:

Step1: Translate shape to origin

For a vertex $(x,y)$ and rotation point $(h,k)$:
$x' = x - h$, $y' = y - k$

Step2: Rotate translated point

Use origin rotation rules:

• 90° clockwise: $(x',y') \to (y', -x')$
• 90° counterclockwise: $(x',y') \to (-y', x')$
• 180°: $(x',y') \to (-x', -y')$
• 270° clockwise: $(x',y') \to (-y', x')$

Step3: Translate back to rotation point

$x'' = x_{rot} + h$, $y'' = y_{rot} + k$

Answer:

The 3-step process for rotating a shape about a non-origin point $(h,k)$ is:

1. Translate all vertices by subtracting the rotation point coordinates: $(x,y) \to (x-h, y-k)$
2. Apply the desired origin rotation rule to the translated coordinates
3. Translate the rotated coordinates back by adding the rotation point coordinates: $(x_{rot}, y_{rot}) \to (x_{rot}+h, y_{rot}+k)$

For example, rotating point $A(-4,-1)$ 90° clockwise about $(h,k)=(1,1)$:
Step1: $(-4-1, -1-1)=(-5,-2)$
Step2: $(-2, 5)$ (90° clockwise origin rule)
Step3: $(-2+1, 5+1)=(-1,6)$ (final rotated point)