Question

If a line segment with endpoints (6, 3)
(
6
,

3
)
and (6, 7)
(
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

0 units
0 units

There is not enough information to measure the line segment.
There is not enough information to measure the line segment.

10 units
10 units

4 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 and then check if the translation affects that length.

The original endpoints of the line segment are (6, 3) and (6, 7). This segment is vertical, and the length can be calculated as follows:

\[
\text{Length} = |y_2 - y_1| = |7 - 3| = |4| = 4 \text{ units}
\]

Now, we apply the translation:
- Translate 3 units up: This changes the y-coordinates from (3) and (7) to (6) + 3 and (7) + 3.
- So the new endpoints are:
- First endpoint: (6, 3 + 3) = (6, 6)
- Second endpoint: (6, 7 + 3) = (6, 10)

- Translate 4 units to the right: This changes the x-coordinates from (6) to (6 + 4).
- So the new endpoints become:
- First endpoint: (6 + 4, 6) = (10, 6)
- Second endpoint: (6 + 4, 10) = (10, 10)

The new endpoints after the translation are (10, 6) and (10, 10).

Now, we can calculate the length of the new line segment:

\[
\text{New Length} = |y_2 - y_1| = |10 - 6| = |4| = 4 \text{ units}
\]

The length of the line segment remains 4 units after the translation.

Therefore, the answer is **4 units**.