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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) Responses A′(7,0),%C2%A0B′(5,−4),%C2%A0C′(10,−2) upper A prime left parenthesis 7 comma 0 right parenthesis ,%C2%A0 upper B prime left parenthesis 5 comma negative 4 right parenthesis ,%C2%A0 upper C prime left parenthesis 10 comma negative 2 right parenthesis A′(−1,2),%C2%A0B′(−3,−2),%C2%A0C′(2,0) upper A prime left parenthesis negative 1 comma 2 right parenthesis ,%C2%A0 upper B prime left parenthesis negative 3 comma negative 2 right parenthesis ,%C2%A0 upper C prime left parenthesis 2 comma 0 right parenthesis A′(1,0),%C2%A0B′(−1,−4),%C2%A0C′(4,−2) upper A prime left parenthesis 1 comma 0 right parenthesis ,%C2%A0 upper B prime left parenthesis negative 1 comma negative 4 right parenthesis ,%C2%A0 upper C prime left parenthesis 4 comma negative 2 right parenthesis A′(1,10),%C2%A0B′(−1,6),%C2%A0C′(4,7)

1 answer

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

If the vertices of triangle ABC are:

  • A(x₁, y₁)
  • B(x₂, y₂)
  • C(x₃, y₃)

After the translation, the new coordinates A', B', and C' will be:

  • A' = (x₁ - 3, y₁ - 5)
  • B' = (x₂ - 3, y₂ - 5)
  • C' = (x₃ - 3, y₃ - 5)

Without the original coordinates of triangle ABC, we cannot calculate the exact new coordinates. However, we can analyze the given options to determine which one corresponds to a possible translation.

Let's check the options.

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

Assuming A(x, y), for the new coordinates after translation:

  • If A(x, y) = A'(x - 3, y - 5)
  • If we take our new coordinates and reverse the transformation:
    • A'(x', y') = A(x' + 3, y' + 5)

Let's check viable options that make sense:

For Option 2: A'(-1, 2),

  • Original A would be calculated as: \[ A(-1 + 3, 2 + 5) = A(2, 7) \]

For B'(-3, -2):

  • Original B would be: \[ B(-3 + 3, -2 + 5) = B(0, 3) \]

For C'(2, 0):

  • Original C would be: \[ C(2 + 3, 0 + 5) = C(5, 5) \]

This transformation follows the rules.

Thus, without knowing the original vertices coordinates, Option 2 A'(-1, 2), B'(-3, -2), C'(2, 0) is correct!