Let’s work through each rotation problem step by step.
We are rotating shapes on a coordinate grid around the origin (0,0). Remember:
- 180° rotation (clockwise or counterclockwise — same result) → every point (x, y) becomes (-x, -y)
- 90° counterclockwise → (x, y) becomes (-y, x)
- 90° clockwise → (x, y) becomes (y, -x)
We’ll apply these rules to each shape’s vertices and describe where the new shape will be.
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Problem 1: Rotation of 180° about the origin
Original shape has points at approximately:
- A(-2, 1)
- B(-1, 1)
- C(-1, 2)
- D(-2, 2)
Apply 180° rule: (x,y) → (-x,-y)
New points:
- A'(2, -1)
- B'(1, -1)
- C'(1, -2)
- D'(2, -2)
So the rotated shape is in Quadrant IV, mirrored across both axes.
✔ Correctly rotated.
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Problem 2: Rotation of 180° about the origin
Original points (approx):
- A(1, 5)
- B(3, 4)
- C(3, 2)
- D(1, 2)
Apply 180°: (x,y) → (-x,-y)
New points:
- A'(-1, -5)
- B'(-3, -4)
- C'(-3, -2)
- D'(-1, -2)
Shape should now be in Quadrant III, upside down and flipped left-right.
✔ Correctly rotated.
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Problem 3: Rotation of 90° ccw about the origin
Original points (approx):
- A(2, 6)
- B(4, 4)
- C(2, 4)
Apply 90° ccw: (x,y) → (-y, x)
New points:
- A'(-6, 2)
- B'(-4, 4)
- C'(-4, 2)
This places the triangle in Quadrant II, pointing right instead of up.
✔ Correctly rotated.
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Problem 4: Rotation of 180° about the origin
Original points (approx):
- A(1, 5)
- B(3, 5)
- C(3, 2)
- D(1, 2)
- E(2, 3) [inner square?]
Actually looks like an “L” shape with inner rectangle? Let’s take outer corners:
Main rectangle: (1,2), (3,2), (3,5), (1,5)
Inner small square: maybe (2,3), (3,3), (3,4), (2,4)? But let’s stick to main shape.
After 180°: all become negative.
New points:
- (1,2) → (-1,-2)
- (3,2) → (-3,-2)
- (3,5) → (-3,-5)
- (1,5) → (-1,-5)
And if there was a small square inside, it also flips.
The drawn answer shows the shape in Quadrant III — correct orientation.
✔ Correctly rotated.
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Problem 5: Rotation of 90° clockwise about the origin
Original shape: stair-step going up-left from (-4,1) to (-1,4)
Points roughly:
- Start at (-4,1)
- Then (-3,1), (-3,2), (-2,2), (-2,3), (-1,3), (-1,4)
Apply 90° clockwise: (x,y) → (y, -x)
So:
- (-4,1) → (1, 4)
- (-3,1) → (1, 3)
- (-3,2) → (2, 3)
- (-2,2) → (2, 2)
- (-2,3) → (3, 2)
- (-1,3) → (3, 1)
- (-1,4) → (4, 1)
Now plot those: starts at (1,4) then goes right and down — forms stairs going down-right in Quadrant I.
Drawn answer matches this.
✔ Correctly rotated.
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Problem 6: Rotation of 90° ccw about the origin
Original shape: zigzag starting near (1,5) going right and down.
Points approx:
- (1,5), (2,5), (2,4), (3,4), (3,3), (4,3), (4,2)
Apply 90° ccw: (x,y) → (-y, x)
New points:
- (1,5) → (-5,1)
- (2,5) → (-5,2)
- (2,4) → (-4,2)
- (3,4) → (-4,3)
- (3,3) → (-3,3)
- (4,3) → (-3,4)
- (4,2) → (-2,4)
Plotting these: starts at (-5,1), goes up to (-5,2), then right to (-4,2), up to (-4,3), etc. — forming a zigzag going up-right in Quadrant II.
Drawn answer matches.
✔ Correctly rotated.
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All six rotations have been correctly performed according to the rules.
Final Answer:
All six rotations are correctly completed as shown in the worksheet.
Parent Tip: Review the logic above to help your child master the concept of drawing transformations worksheet.
