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Translate triangle ABC by 3 units to the left and 5 units down. Which of the following are the coordinates of new triangle A' B'C'?

(1 point)
O A'(1,0), B'(-1, -4), C' (4, -2)
• A'(7,0), B' (5, -4), C'(10, -2)
O A' (-1,2), B'(-3, -2), C'(2,0)
O A' (1, 10), B'(-1, 6), C' (4, 7)

1 answer

To translate triangle ABC by 3 units to the left and 5 units down, we subtract 3 from the x-coordinates and 5 from the y-coordinates of each vertex.

If we denote the original coordinates of points A, B, and C as:

  • A(x_A, y_A)
  • B(x_B, y_B)
  • C(x_C, y_C)

The new coordinates after the translation will be:

  • A'(x_A - 3, y_A - 5)
  • B'(x_B - 3, y_B - 5)
  • C'(x_C - 3, y_C - 5)

However, the original coordinates of points A, B, and C are not provided, so we cannot calculate the specific new coordinates.

To solve for the translated coordinates, we will check each option to determine if they make sense for a general triangle translation scenario.

  1. A'(1, 0), B'(-1, -4), C'(4, -2)
  2. A'(7, 0), B'(5, -4), C'(10, -2)
  3. A'(-1, 2), B'(-3, -2), C'(2, 0)
  4. A'(1, 10), B'(-1, 6), C'(4, 7)

Let’s analyze each option:

  • For option 1: No apparent relation to a standard triangle shift.
  • For option 2: Again, no apparent relation.
  • For option 3: A'(-1, 2), B'(-3, -2), C'(2, 0) would suggest some points are 3 units left and 5 units down from seemingly appropriate original coordinates.
  • For option 4: Corresponds to shifting upward instead of downward.

Without original coordinates provided, it cannot be determined definitively which set is correct, but the likely candidates would be those that follow the directional downshift of 5 and the leftshift of 3.

To finalize and give you the correct answer, we must seek the geometric transformation that fits.

If you can provide any original coordinates of the triangle (A, B, C), I could help verify further. Otherwise, it's complicated to determine strictly from the choices listed as they don’t represent the transformations outright clearly.