Question

If a line segment with endpoints and is translated 3 units up and 4 units to the
right, how long is the line segment after the translation?(1 point)
(6, 3) ( 6, 3 ) (6, 7) ( 6, 7 )
There is not enough information to measure the line segment.
4 units
10 units
0 units

Answer 1

To determine the length of the line segment after the translation, we first need to find the original length of the line segment defined by the endpoints \((6, 3)\) and \((6, 7)\).

The length of a line segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the distance formula:

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

In this case:

- \((x_1, y_1) = (6, 3)\)
- \((x_2, y_2) = (6, 7)\)

Plugging in the coordinates:

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

Now, we perform the translation. Translating the line segment 3 units up and 4 units to the right will not change its length. The new endpoints of the segment will be:

- From \((6, 3)\) to \((6 + 4, 3 + 3) = (10, 6)\)
- From \((6, 7)\) to \((6 + 4, 7 + 3) = (10, 10)\)

After the translation, we can again use the distance formula:

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

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

So the answer is **4 units**.