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 with endpoints (6, 3) and (6, 7), we can use the distance formula. However, since we know that both points have the same x-coordinate (6), we can simply find the difference in the y-coordinates:

Length = |y2 - y1| = |7 - 3| = 4 units.

Next, we will translate the line segment 3 units up and 4 units to the right. This affects the endpoints as follows:

1. The point (6, 3) translated becomes:

   • x-coordinate: 6 + 4 = 10
   • y-coordinate: 3 + 3 = 6
   • New point: (10, 6)

2. The point (6, 7) translated becomes:

   • x-coordinate: 6 + 4 = 10
   • y-coordinate: 7 + 3 = 10
   • New point: (10, 10)

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

Length = |y2 - y1| = |10 - 6| = 4 units.

So, the length of the line segment after the translation remains 4 units. Thus, the answer is:

4 units.