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In order to know the distance of two points we need to perform the Pythagorean Theorem which is:

This is where a and b are the legs of the triangle and c is the hypotenuse. (This theorem only works in right triangles, triangles with an angle of measure 90°)

In a Cartesian plane the coordinates of two points would be (x_a,y_a) and (x_b,y_b) this would translate the Pythagorean Theorem into:

What we need in the problem is the value of c so we know that (x_a,y_a)=(1,3) and (x_b,y_b)=(4,7).

We substitute the values into the Pythagorean Theorem and get:
c^2=(1-4)^2+(3-7)^2 \\ =(-3)^3+(-4)^2 \\ =9+16 \\ =25

We know now that the square of the distance of the points is 25 so the distance is either +5 or -5 but since a distance is always positive the distance is 5.