# What is the distance between the points (1, 3) and (4, 7)?

1
by freddyappl893

2015-05-12T18:46:07+08:00

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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  and  this would translate the Pythagorean Theorem into:

What we need in the problem is the value of c so we know that  and .

We substitute the values into the Pythagorean Theorem and get:

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.