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)
• 10 units
There is not enough information to measure the line segment.
• 4 units
• units

Answer 1

To determine the length of the line segment after translation, we first need to calculate the length of the original line segment with endpoints (6, 3) and (6, 7).

The formula for the length of a line segment between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

For the endpoints (6, 3) and (6, 7):

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

Calculating the length:

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

The length of the original line segment is 4 units.

Next, we translate the line segment 3 units up and 4 units to the right. The new endpoints after translation will be:

- The point (6, 3) becomes \((6 + 4, 3 + 3) = (10, 6)\)
- The point (6, 7) becomes \((6 + 4, 7 + 3) = (10, 10)\)

Now, we find the length of the translated line segment with endpoints (10, 6) and (10, 10):

Using the same formula for length:

\[
L' = \sqrt{(10 - 10)^2 + (10 - 6)^2} = \sqrt{0^2 + 4^2} = \sqrt{16} = 4
\]

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

Therefore, the correct answer is: **4 units**.