Question

f 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

4 units
4 units

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

0 units

Answer 1

To find the length of a line segment, we can use the distance formula, but first, let's check what happens when the segment is translated.

The endpoints of the line segment are:
- A(6, 3)
- B(6, 7)

### Step 1: Length before translation

The length of the line segment before translation can be calculated as follows:

Using the distance formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Here, the coordinates of the endpoints are:
- \( (x_1, y_1) = (6, 3) \)
- \( (x_2, y_2) = (6, 7) \)

Plugging the values into the formula:
\[
d = \sqrt{(6 - 6)^2 + (7 - 3)^2} = \sqrt{0 + 4^2} = \sqrt{16} = 4
\]

So, the length of the line segment before translation is **4 units**.

### Step 2: Translation of the endpoints

Now we translate the line segment:
- Move 3 units up: This adds 3 to the y-coordinates.
- Move 4 units to the right: This adds 4 to the x-coordinates.

New coordinates after translation:
- A'(6 + 4, 3 + 3) = A'(10, 6)
- B'(6 + 4, 7 + 3) = B'(10, 10)

### Step 3: Length after translation

Now, let's calculate the length of the translated line segment using the new endpoints A'(10, 6) and B'(10, 10):
\[
d = \sqrt{(10 - 10)^2 + (10 - 6)^2} = \sqrt{0 + 4^2} = \sqrt{16} = 4
\]

### Conclusion

The length of the line segment remains **4 units** after the translation. Therefore, the correct response is:

**4 units**.