To translate triangle ABC by 3 units to the left and 5 units down, we will decrease the x-coordinates by 3 and the y-coordinates by 5 for each vertex.
Let's denote the original coordinates of the vertices of triangle ABC as:
- A(x1, y1)
- B(x2, y2)
- C(x3, y3)
After the translation, the new coordinates (A', B', C') will be:
- A′(x1 - 3, y1 - 5)
- B′(x2 - 3, y2 - 5)
- C′(x3 - 3, y3 - 5)
Now, we need to check which option represents the translated triangle A'B'C'.
To find A', B', and C', let's review each of the response options:
- A′(7, 0), B′(5, −4), C′(10, −2)
- A′(1, 10), B′(−1, 6), C′(4, 7)
- A′(−1, 2), B′(−3, −2), C′(2, 0)
- A′(1, 0), B′(−1, −4), C′(4, −2)
Without the original coordinates of triangle ABC, we can't determine the correct translation. However, we know that:
- To obtain the new coordinates:
- Track the change for x and y: new_x = original_x - 3 and new_y = original_y - 5.
To determine which coordinates (A′B′C′) could correspond to the translation for some original vertices, you can select any of the given options and verify if choosing x and y values per coordinate correctly yields a change of -3 and -5 from any other coordinate set respectively.
Since we don't have those values specified, we cannot definitively determine which coordinates belong to A'B'C' based on triangle ABC.
If you have the original coordinates of triangle ABC, please provide them, and we can determine the correct new coordinates after the translation. Otherwise, to find the correct transformed coordinates based on options:
If we were to calculate the translation on a hypothetical triangle whose coordinates could yield the described translation on any option, we can evaluate against those expectations.
If we analyze the options, the most plausible option reflecting any original vertices translated to correct integers after our operations should ideally yield y-values significantly lower than original positive integers, so we would guess and check against that specific operation.
The choice with negative values is A′(−1, 2), B′(−3, −2), C′(2, 0) would be plausible as those integers exhibit potential translation values.
To confirm definitively, we need the original triangle coordinates before the translation.