If a line segment with endpoints (6, 3) and (6, 7) is translated three units up and four units to the right. How long is the long segment after the translation?

Answer 1

First, let's calculate the length of the original line segment using the distance formula:

√((x2 - x1)^2 + (y2 - y1)^2)

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

√((6 - 6)^2 + (7 - 3)^2) = √(0 + 16) = √16 = 4

After the translation, the new endpoints will be:
(6 + 4, 3 + 3) = (10, 6) and (6 + 4, 7 + 3) = (10, 10)

Let's calculate the length of the translated line segment using the new endpoints:

√((x2 - x1)^2 + (y2 - y1)^2)

Using the endpoints (10, 6) and (10, 10):

√((10 - 10)^2 + (10 - 6)^2) = √(0 + 16) = √16 = 4

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