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 point)
1.there is not enough information to measure the line segment
2.4 units
3.0 units
4.10 units
The line segment has endpoints (6, 3) and (6, 7). When it is translated 3 units up, the new endpoints will be (6, 6) and (6, 10). Then, when it is translated 4 units to the right, the new endpoints will be (10, 6) and (10, 10).
Using the distance formula, we can calculate the length of the line segment:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
d = sqrt((10 - 6)^2 + (10 - 6)^2)
d = sqrt(4^2 + 4^2)
d = sqrt(16 + 16)
d = sqrt(32)
d ≈ 5.66
Therefore, the length of the line segment after the translation is approximately 5.66 units. So, the closest answer choice is 6.
To find the length of the line segment after the translation, we can use the distance formula.
The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distance using the given endpoints and the translation of 3 units up and 4 units to the right.
Endpoint 1 (6, 3) translated 3 units up and 4 units to the right:
New endpoint 1: (6 + 4, 3 + 3) = (10, 6)
Endpoint 2 (6, 7) translated 3 units up and 4 units to the right:
New endpoint 2: (6 + 4, 7 + 3) = (10, 10)
Now, let's calculate the new length of the line segment.
d = √((10 - 10)^2 + (10 - 6)^2)
= √(0^2 + 4^2)
= √(16)
= 4
Therefore, the length of the line segment after the translation is 4 units.
The correct answer is option 2. 4 units.