If a line segment with endpoint (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?
The length of a line segment is equal to the distance between its endpoints.
The distance between two points (x1, y1) and (x2, y2) is given by the formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
For the given line segment with endpoint (6,3) and (6,7), the length is:
distance = sqrt((6 - 6)^2 + (7 - 3)^2)
= sqrt(0 + 16)
= sqrt(16)
= 4
After the translation of 3 units up and 4 units to the right, the new endpoint will be (6 + 4, 7 + 3) = (10, 10).
The distance between the translated endpoints (6,3) and (10,10) is:
distance = sqrt((10 - 6)^2 + (10 - 3)^2)
= sqrt(16 + 49)
= sqrt(65)
So, the length of the line segment after the translation is sqrt(65) or approximately 8.06 units.