Coordinate Transformations · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Reflecting, Rotating, and Translating on a Grid

Mathematics · Geometry · ages 11-14
Name ______________________   Date ____________

  1. Point E is at (-4, 1). It slides 2 units right and 5 units down. Where does it land?

    • (-2, -4)
    • (-6, 6)
    • (2, -4)
    • (-2, 6)

  2. Point D is at (2, -5). It slides 4 units left and 3 units up. What is its new x-coordinate?

    Answer: ______________

  3. Point A is at (3, 4). Reflect A in the line y = x. What are the coordinates of the image?

    • (4, 3)
    • (3, -4)
    • (-4, -3)

  4. After you translate a shape by a vector, its side lengths and angles stay exactly the same as before.

    Circle one:   True   False

  5. Point (4,1) rotates 180 degrees about the origin. What is the sum of its new coordinates?

    Answer: ______________

  6. Point C is at (-4, 7). Reflect C in the line y = x. What is the image?

    • (7, -4)
    • (-7, 4)
    • (4, -7)

  7. Point F is at (5, 2). Reflect it in the vertical line x = 1. Where does it land?

    • (-3, 2)
    • (7, 2)
    • (3, 2)
    • (-3, -2)

  8. Leo translates a shape and says all lengths and angles stay the same; only the position changes. Is Leo right?

    Circle one:   True   False

  9. Zak translates a rectangle 4 units right and 3 units up. He says the new rectangle is bigger because it ended up farther from the origin. What is wrong with his reasoning?

    • He used the wrong vector
    • Distance from the origin can change, but the rectangle's size does not, so it isn't bigger
    • The rectangle actually got smaller, not bigger

  10. Triangle (1,1), (4,1), (1,3) rotates 180 degrees about (0,0). Where does (4,1) land?

    • (4,-1)
    • (-1,-4)
    • (-4,-1)
    • (1,-4)
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Reflecting, Rotating, and Translating on a Grid W1-mt_K0Y15w48SY-s1

  1. (-2, -4) · Add 2 to x and subtract 5 from y: (-4 + 2, 1 - 5) = (-2, -4).
  2. -2 · Moving 4 units left subtracts 4 from x: 2 - 4 = -2. Moving up changes y, not x.
  3. (4, 3) · Reflecting in y = x swaps the x and y coordinates, so (3, 4) becomes (4, 3).
  4. True · A translation only slides the shape. It doesn't stretch, shrink, or turn it, so lengths and angles don't change.
  5. -5 · Half turn flips both signs to (-4,-1), and -4 + -1 = -5.
  6. (7, -4) · Swap the coordinates of (-4, 7) to get (7, -4).
  7. (-3, 2) · The point is 4 units right of x = 1, so its image is 4 units left of that line. Its x-coordinate is -3 and y stays 2.
  8. True · Leo is right: translations are rigid motions.
  9. Distance from the origin can change, but the rectangle's size does not, so it isn't bigger · A translation only changes position. Even though the shape moved farther from the origin, every side length and angle stayed the same, so it's congruent to the original, not bigger.
  10. (-4,-1) · Half turn negates both coordinates: (-4,-1).
Worksheet · LightMySky