Ask a New Question
Menu

Use the function rules to find the coordinates of ДА" B" C" and predict the quadrant it will be in after the transformations. ABC, with coordinates A (-8,4), B (-5,8), and C (-3, 3), is transformed by (x, y) → (x + 4, y - 6) to produce AA' B'C". AA' B'C' is transformed by the rule (x, y) → (x + 5, y - 3). Create the rule for the composition transformation and predict what quadrant the image will be in.

(4 points) Make real short please

3 answers

To find the coordinates of points A', B', and C' after the transformations, we apply the transformation rules sequentially.

  1. First Transformation: (x, y) → (x + 4, y - 6)

    • A' = (-8 + 4, 4 - 6) = (-4, -2)
    • B' = (-5 + 4, 8 - 6) = (-1, 2)
    • C' = (-3 + 4, 3 - 6) = (1, -3)

  2. Second Transformation: (x, y) → (x + 5, y - 3)

    • A'' = (-4 + 5, -2 - 3) = (1, -5)
    • B'' = (-1 + 5, 2 - 3) = (4, -1)
    • C'' = (1 + 5, -3 - 3) = (6, -6)

Final Coordinates:

  • A'' (1, -5)
  • B'' (4, -1)
  • C'' (6, -6)

Composition Rule: To combine the transformations:

  • Start (x, y) → (x + 4, y - 6) → (x + 9, y - 9)

Predicted Quadrant: Since all final coordinates have positive x-values and negative y-values, the image will be in Quadrant IV.

Shorter

  1. Transformations:

    • A → A': (-8, 4) → (-4, -2)

    • B → B': (-5, 8) → (-1, 2)

    • C → C': (-3, 3) → (1, -3)

    • A' → A'': (-4, -2) → (1, -5)

    • B' → B'': (-1, 2) → (4, -1)

    • C' → C'': (1, -3) → (6, -6)

  2. Final Coordinates:

    • A'' (1, -5), B'' (4, -1), C'' (6, -6)

  3. Composition Rule:

    • Combined: (x, y) → (x + 9, y - 9)

  4. Quadrant:

    • The image is in Quadrant IV.