Question

f 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 10 units 10 units 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

Answer 1

To find the length of the line segment after it has been translated, we first need to determine the length of the segment before the translation.

The endpoints of the line segment are \((6, 3)\) and \((6, 7)\).

We can calculate the length of the line segment using the distance formula. Since both points have the same x-coordinate, the distance can simply be calculated by subtracting the y-coordinates:

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

Next, we translate the endpoints 3 units up and 4 units to the right.

- Translating the point \((6, 3)\):
- New coordinates: \((6 + 4, 3 + 3) = (10, 6)\)

- Translating the point \((6, 7)\):
- New coordinates: \((6 + 4, 7 + 3) = (10, 10)\)

Now, we have the new endpoints of the line segment as \((10, 6)\) and \((10, 10)\).

We can calculate the new length of the line segment in the same way as before:

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

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

So the correct response is:

**4 units**