Let’s go through each problem one by one. We’ll figure out what the transformation does, and then either graph the new shape (for problems 1–4) or write a rule that describes how the points moved (for problems 5–6).
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Problem 1: Rotation 90° counterclockwise about the origin
Original points:
- J is at (-4, 1)
- K is at (-5, -1)
- L is at (-1, -2)
Rule for 90° counterclockwise rotation about origin:
(x, y) → (-y, x)
Apply to each point:
- J(-4, 1) → (-1, -4)
- K(-5, -1) → (1, -5)
- L(-1, -2) → (2, -1)
So the new triangle has vertices at (-1, -4), (1, -5), and (2, -1). You’d plot those on the grid.
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Problem 2: Translation 4 units right and 1 unit down
Original points:
- A is at (-3, 3)
- B is at (-3, 1)
- C is at (-2, 2)
Translation rule: (x, y) → (x + 4, y - 1)
Apply:
- A(-3, 3) → (1, 2)
- B(-3, 1) → (1, 0)
- C(-2, 2) → (2, 1)
Plot these new points to get the translated triangle.
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Problem 3: Translation 1 unit right and 1 unit up
Original points:
- I is at (-3, -1)
- J is at (0, 0)
- K is at (3, -1)
- L is at (0, -3)
Rule: (x, y) → (x + 1, y + 1)
Apply:
- I(-3, -1) → (-2, 0)
- J(0, 0) → (1, 1)
- K(3, -1) → (4, 0)
- L(0, -3) → (1, -2)
Plot these to get the new quadrilateral.
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Problem 4: Reflection across the x-axis
Original points:
- A is at (1, -3)
- B is at (0, 1)
- C is at (-2, 1)
- D is at (-3, 0)
Reflection over x-axis rule: (x, y) → (x, -y)
Apply:
- A(1, -3) → (1, 3)
- B(0, 1) → (0, -1)
- C(-2, 1) → (-2, -1)
- D(-3, 0) → (-3, 0)
Plot these to get the reflected figure.
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Problem 5: Write a rule describing the transformation
Look at original triangle ABC and image A'B'C':
Original:
- A(-2, -3)
- B(-3, -4)
- C(-1, -2)
Image:
- A'(-1, -2)
- B'(-2, -3)
- C'(0, -1)
Compare:
- A(-2, -3) → A'(-1, -2): x increased by 1, y increased by 1
- B(-3, -4) → B'(-2, -3): same — +1, +1
- C(-1, -2) → C'(0, -1): same — +1, +1
So the rule is:
(x, y) → (x + 1, y + 1)
That’s a translation 1 unit right and 1 unit up.
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Problem 6: Write a rule describing the transformation
Original square PQRS:
- P(1, 0)
- Q(2, 0)
- R(2, 2)
- S(1, 2)
Image P'Q'R'S':
- P'(3, 0)
- Q'(4, 0)
- R'(4, 2)
- S'(3, 2)
Compare:
- P(1, 0) → P'(3, 0): x +2, y unchanged
- Q(2, 0) → Q'(4, 0): x +2
- R(2, 2) → R'(4, 2): x +2
- S(1, 2) → S'(3, 2): x +2
So the rule is:
(x, y) → (x + 2, y)
That’s a translation 2 units right.
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Final Answer:
1) Plot points (-1, -4), (1, -5), (2, -1)
2) Plot points (1, 2), (1, 0), (2, 1)
3) Plot points (-2, 0), (1, 1), (4, 0), (1, -2)
4) Plot points (1, 3), (0, -1), (-2, -1), (-3, 0)
5) (x, y) → (x + 1, y + 1)
6) (x, y) → (x + 2, y)
Parent Tip: Review the logic above to help your child master the concept of math worksheet kuta.
