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

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

0 units
0 units

4 units
4 units

10 units

Answer 1

To find the length of the line segment with endpoints (6, 3) and (6, 7), we first calculate its original length.

The length of a line segment can be determined using the distance formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Substituting the endpoints (6, 3) and (6, 7):
- \(x_1 = 6, y_1 = 3\)
- \(x_2 = 6, y_2 = 7\)

Now, we calculate the length:
\[
d = \sqrt{(6 - 6)^2 + (7 - 3)^2} = \sqrt{0 + (4)^2} = \sqrt{16} = 4 \text{ units}
\]

Next, we consider the translation. Translating the line segment 3 units up and 4 units to the right means we add these values to the coordinates of both endpoints.

The new endpoints after translation are:
- From (6, 3) to \((6 + 4, 3 + 3) = (10, 6)\)
- From (6, 7) to \((6 + 4, 7 + 3) = (10, 10)\)

Now, we calculate the length of the translated segment:
Using the new endpoints (10, 6) and (10, 10):

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

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

The correct response is:
**4 units**.