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

10 units
10 units

0 units
0 units

4 units
4 units

There is not enough information to measure the line segment.

Answer 1

The length of the line segment does not change when it is translated.

To find the length of the original line segment with endpoints (6, 3) and (6, 7), we can use the distance formula:

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

Substituting the coordinates of the endpoints:

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

After translating the line segment 3 units up and 4 units to the right, the new endpoints will be:

- The new endpoint for (6, 3) will be (10, 6).
- The new endpoint for (6, 7) will be (10, 10).

Using the distance formula again for the new endpoints:

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

Thus, the length of the line segment after the translation is **4 units**.