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
A: 0 units
B: There is not enough information to measure the line segment
C: 10 units
D: 4 units
To find the length of the line segment after the translation, we can use the distance formula.
The original line segment has endpoints (6,3) and (6,7). The difference in the y-coordinates is 7 - 3 = 4. The difference in the x-coordinates is 6 - 6 = 0.
After the translation 3 units up and 4 units to the right, the new line segment will have endpoints (6 + 4, 3 + 3) = (10, 6) and (6 + 4, 7 + 3) = (10, 10).
The difference in the y-coordinates of the new line segment is 10 - 6 = 4. The difference in the x-coordinates of the new line segment is 10 - 10 = 0.
Using the distance formula, the length of the new line segment is √((0)^2 + (4)^2) = √(0 + 16) = √16 = 4 units.
Therefore, the answer is D: 4 units