Final answer:
The length of the line segment between (-5,2) and (1,4) is 2√10 units.
Step-by-step explanation:
To find the length of a line segment, we can use the distance formula. The distance formula is derived from the Pythagorean theorem and it calculates the distance between two points in a coordinate plane.
Using the distance formula, we can find the length of the line segment between (-5,2) and (1,4):
d = √((x2 - x1)^2 + (y2 - y1)^2)
Substituting the coordinates, we get:
d = √((1 - (-5))^2 + (4 - 2)^2)
Simplifying further:
d = √((6)^2 + (2)^2)
d = √(36 + 4)
d = √40
d = 2√10
Therefore, the length of the line segment is 2√10 units.