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

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

4 units
4 units

0 units
0 units

10 units

Answer 1

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

The endpoints of the line segment are (6, 3) and (6, 7). The length of a vertical line segment can be found by taking the difference of the y-coordinates of its endpoints:

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

Now, we perform the translation. The translation moves every point 3 units up and 4 units to the right. Therefore, we will translate the endpoints as follows:

1. (6, 3) after translation:
- x-coordinate: \(6 + 4 = 10\)
- y-coordinate: \(3 + 3 = 6\)
- New point: (10, 6)

2. (6, 7) after translation:
- x-coordinate: \(6 + 4 = 10\)
- y-coordinate: \(7 + 3 = 10\)
- New point: (10, 10)

Now the new endpoints are (10, 6) and (10, 10). The length of the translated line segment is still the same as before since the translation does not affect the length of the line segment.

Thus, we can calculate the length of the new line segment in the same way:

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

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