If a line segment with endpoints (6, 3) and (6, 7) is translated 3 units up and 4 units to the right, how long is the line segment after the translation?
1. 4 units
2. 10 units
3. 0 units
4. There is not enough information to measure the line segment.
The line segment is translated 3 units up and 4 units to the right. This means that for both endpoints, the x-coordinate is increased by 4 and the y-coordinate is increased by 3.
For the endpoint (6, 3), the translation results in the new endpoint of (6 + 4, 3 + 3) = (10, 6).
For the endpoint (6, 7), the translation results in the new endpoint of (6 + 4, 7 + 3) = (10, 10).
Thus, the new endpoints are (10, 6) and (10, 10).
To find the length of the line segment after the translation, we can use the distance formula.
The distance between the two endpoints is given by:
√[(10 - 10)^2 + (10 - 6)^2]
√[0 + 16]
√16
= 4 units
Therefore, the length of the line segment after the translation is 4 units.
Hence, the correct answer is option 1.