Expand menu menu_open Minimize Start chapters Home History history History expand_more
{{ item.displayTitle }}
navigate_next
No history yet!
Progress & Statistics equalizer Progress expand_more
Student
navigate_next
Teacher
navigate_next
{{ filterOption.label }}
{{ item.displayTitle }}
{{ item.subject.displayTitle }}
arrow_forward
No results
{{ searchError }}
search
menu_open
{{ courseTrack.displayTitle }}
{{ statistics.percent }}% Sign in to view progress
{{ printedBook.courseTrack.name }} {{ printedBook.name }}
search Use offline Tools apps
Login account_circle menu_open

Distance Formula

Proof

Distance Formula

If and are two points in a coordinate plane, the distance between them, can be found.

The horizontal and vertical distance between the points can be thought of as and respectively.

As can be seen in the diagram above, which gives the distance between points and is the hypotenuse of the right triangle whose legs are and An equation can be created for using the Pythagorean Theorem, and are the differences between the coordinates of the points. They can be written as and Here, the absolute values are included to ensure the distances are positive. Rearranging the equation and substituting these values gives the following.

Because squares are always positive, the absolute value bars can be removed. Then, can be isolated.

Since is a distance, it is always positive. Therefore, the negative solution can be omitted.
Q.E.D.