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

4 units
4 units

10 units
10 units

0 units
0 units

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

Answer 1

To find the length of the line segment, we first need to determine its original length. The endpoints of the line segment are (6, 3) and (6, 7).

The length of a vertical line segment can be calculated using the formula for the distance between two points, specifically focusing on their y-coordinates since the x-coordinates are the same:

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

Next, we will apply the translation that moves the line segment 3 units up and 4 units to the right. This will change the endpoints:

- The original point (6, 3) becomes:
\[
(6 + 4, 3 + 3) = (10, 6)
\]

- The original point (6, 7) becomes:
\[
(6 + 4, 7 + 3) = (10, 10)
\]

Now the new endpoints after the translation are (10, 6) and (10, 10). We can again calculate the length of this new line segment:

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

So, after the translation, the length of the line segment remains 4 units.

Therefore, the answer is:

**4 units**