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To find the distance of two points we need to use the Pythagorean Theorem the distance between points is a hypotenuse of a right triangle.

The Pythagorean Theorem states that:

The Pythagorean Theorem triangles with 90° (right triangles) a and b are the side lengths of the legs while c is the length of the hypotenuse.

In a Cartesian plane the side lengths a and b are represented like this:
(x_a-y_a)=a \\ (x_b-yb)=b

So the Pythagorean Theorem would be:

We have (x_a,y_a) as the coordinates of point A which is (-2,3)
and (x_b,y_b) as the coordinates of point B which is (4,1)

We substitute the values to the Pythagorean theorem:
c^2=(-2-4)^2+(3-1)^2 \\ =(-6)^2+(2)^2 \\ =36+4 \\ =40

c= \sqrt{40} =2 \sqrt{10}

Therefore the length of the line segment is 2 \sqrt{10}  
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