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

0 units
0 units

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

10 units
10 units

Answer 1

To find the length of the line segment after translation, we first determine the original length of the segment.

The endpoints of the segment are \((6, 3)\) and \((6, 7)\). We can use the distance formula to calculate the distance between two points:

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

Substituting the coordinates into the formula:

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

Now we translate the endpoints of the line segment 3 units up and 4 units to the right.

The new coordinates after translation are:

1. For the point \((6, 3)\):
\[
(6 + 4, 3 + 3) = (10, 6)
\]

2. For the point \((6, 7)\):
\[
(6 + 4, 7 + 3) = (10, 10)
\]

Now, we calculate the length of the new line segment with endpoints \((10, 6)\) and \((10, 10)\):

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

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