Michelle translates a line up three units and to the right two units if two points on the original line are (1, -5) and (4, -4) what are these two points following the translation?
To translate a point up by three units, we add 3 to its y-coordinate. Similarly, to translate a point to the right by two units, we add 2 to its x-coordinate.
Given the original points are (1,-5) and (4,-4), we can apply the translation as follows:
For the point (1,-5):
- Translating up three units results in the new y-coordinate: -5 + 3 = -2
- Translating to the right two units results in the new x-coordinate: 1 + 2 = 3
So, the new coordinates for the first point after the translation are (3, -2).
For the point (4,-4):
- Translating up three units results in the new y-coordinate: -4 + 3 = -1
- Translating to the right two units results in the new x-coordinate: 4 + 2 = 6
So, the new coordinates for the second point after the translation are (6, -1).
To find the two points after the translation, we need to apply the given translation to each of the original points.
Translation: up three units and to the right two units
Let's start with the first point (1, -5):
Translation for the x-coordinate: +2 units
Translation for the y-coordinate: +3 units
Updated x-coordinate: 1 + 2 = 3
Updated y-coordinate: -5 + 3 = -2
So, the first point after the translation is (3, -2).
Now, let's consider the second point (4, -4):
Translation for the x-coordinate: +2 units
Translation for the y-coordinate: +3 units
Updated x-coordinate: 4 + 2 = 6
Updated y-coordinate: -4 + 3 = -1
Therefore, the second point after the translation is (6, -1).
To summarize:
The two points following the translation are (3, -2) and (6, -1).