The worksheet is focused on applying rotations of points on the coordinate plane about the origin. Let's go through each transformation step-by-step, completing any missing coordinates:

1) Rotation 180° about the origin

For rotation 180°: $(x, y) \rightarrow (-x, -y)$

• $S(-1, -3) \rightarrow S' = (1, 3)$
• $T(3, 0) \rightarrow T' = (-3, 0)$
• $U(2, 5) \rightarrow U' = (-2, -5)$

Coordinates:

• $S'(1, 3)$, $T'(-3, 0)$, $U'(-2, -5)$

2) Rotation 90° counterclockwise about the origin

For 90° counterclockwise: $(x, y) \rightarrow (-y, x)$

• $W(3, -2) \rightarrow W' = (2, 3)$
• $X(-2, -1) \rightarrow X' = (1, -2)$
• $Y(2, -3) \rightarrow Y' = (3, 2)$

Coordinates:

• $W'(2, 3)$, $X'(1, -2)$, $Y'(3, 2)$

3) Rotation 180° about the origin

For rotation 180°: $(x, y) \rightarrow (-x, -y)$

• $L(-3, -5) \rightarrow L' = (3, 5)$
• $K(-4, -1) \rightarrow K' = (4, 1)$
• $J(0, -2) \rightarrow J' = (0, 2)$

Coordinates:

• $L'(3, 5)$, $K'(4, 1)$, $J'(0, 2)$

4) Rotation 90° clockwise about the origin

For 90° clockwise: $(x, y) \rightarrow (y, -x)$

• $K(4, -5) \rightarrow K' = (-5, -4)$
• $J(5, -3) \rightarrow J' = (-3, -5)$
• $I(5, -5) \rightarrow I' = (-5, -5)$

Coordinates:

• $K'(-5, -4)$, $J'(-3, -5)$, $I'(-5, -5)$

5) Rotation 180° about the origin

For rotation 180°: $(x, y) \rightarrow (-x, -y)$

• $J(1, -2) \rightarrow J' = (-1, 2)$
• $I(1, 2) \rightarrow I' = (-1, -2)$
• $H(3, -3) \rightarrow H' = (-3, 3)$

Coordinates:

• $J'(-1, 2)$, $I'(-1, -2)$, $H'(-3, 3)$

6) Rotation 90° counterclockwise about the origin

For 90° counterclockwise: $(x, y) \rightarrow (-y, x)$

• $H(-5, -2) \rightarrow H' = (2, -5)$
• $G(-3, 0) \rightarrow G' = (0, -3)$
• $F(0, -4) \rightarrow F' = (4, 0)$

Coordinates:

• $H'(2, -5)$, $G'(0, -3)$, $F'(4, 0)$

Do you want further clarification on any of these steps?
Here are five related questions to help you practice:

1. What is the rule for rotating a point 270° counterclockwise about the origin?
2. How do you determine the center of rotation in a transformation?
3. If a point lies on the origin, how does it behave under any rotation?
4. What is the effect of multiple consecutive rotations (e.g., two 90° clockwise rotations)?
5. Can the same rules be applied for rotations about a different center?

Tip: Always plot the original and rotated points on the grid to double-check your work!