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