Question

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) Responses There is not enough information to measure the line segment. There is not enough information to measure the line segment. 0 units 0 units 4 units 4 units 10 units

Answer 1

To find the length of the line segment after translation, we first need to determine the length of the original line segment.

The endpoints of the original line segment are (6, 3) and (6, 7). We can find the length of the line segment using the distance formula, which is:

\[
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Substituting the coordinates of the endpoints:

\[
\text{Distance} = \sqrt{(6 - 6)^2 + (7 - 3)^2} = \sqrt{0^2 + (4)^2} = \sqrt{16} = 4
\]

Thus, the length of the original line segment is 4 units.

Next, we apply the translation of 3 units up and 4 units to the right to both endpoints:

1. For the point (6, 3):
- Translating up by 3 units: 3 + 3 = 6
- Translating right by 4 units: 6 + 4 = 10
- New coordinates: (10, 6)

2. For the point (6, 7):
- Translating up by 3 units: 7 + 3 = 10
- Translating right by 4 units: 6 + 4 = 10
- New coordinates: (10, 10)

Now, we calculate the length of the new line segment with the endpoints (10, 6) and (10, 10):

Using the distance formula again:

\[
\text{Distance} = \sqrt{(10 - 10)^2 + (10 - 6)^2} = \sqrt{0^2 + (4)^2} = \sqrt{16} = 4
\]

Therefore, the length of the line segment after the translation is still 4 units.

The correct response is **4 units**.