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 10 units 10 units 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

Answer 1

To find the length of the line segment after translation, we should first calculate the length of the original line segment and then note that translation does not change the length of a line segment.

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

To find the length of the line segment, we can use the distance formula:
\[
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Here, \((x_1, y_1) = (6, 3)\) and \((x_2, y_2) = (6, 7)\).

Calculating the distance:
\[
\text{Distance} = \sqrt{(6 - 6)^2 + (7 - 3)^2} = \sqrt{0 + (4)^2} = \sqrt{16} = 4 \text{ units}
\]

Now, regardless of the translation (3 units up and 4 units to the right), the length of the line segment remains the same.

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