Given the coordinates of the endpoints of a line segment, we can use Pythagoras' Theorem to find its length.
A right-angled triangle is needed.
The x-part of the right-angled triangle will be the difference of the x-coordinates of each endpoint.
The y-part of the right-angled triangle will be the difference of the y-coordinates of each endpoint.
Find the length of the line segment whose endpoints are at (-4, -3) and (2, 4)
The x-part is the difference between -4 and 2, which is is -4 - 2 = -6, so we use 6 as the distance.
The y-part is the difference between -3 and 4, which is is -3 - 4 = -7, so we use 7 as the distance.
This is shown in the diagram below, where the length of the line segment is marked as d.
Using Pythagoras' Theorem, we get:
d2 = 62 + 72
d2 = 36 + 49 = 85
d = √85 = 9.22 units