Examples | Exercises

Objective:
To find the distance between any two points.

To find the distance between two points in a coordinate plane, if they lie on the same vertical or horizontal line, is determined by their coordinates.

A = (x1, y1) and B = (x2, y2) are two points on the plane, then let C = (x2, y1) as in the figure above. The points A, B, C then form a triangle with a right angle at C. The Pythagorean theorem tells us that

[d(A, B)]2 = [d(A, C)]2 + [d(C, B)]2
= |x2 - x1|2 + |y2 - y1|2

From whence, we obtain the distance formula.

The distance between two points A = (x1, y1) and B = (x2, y2) is given by
d(A, B) = SQRT(x2 - x1)2 + (y2 - y1)2

Top | Exercises
EXAMPLE I
Find the distance between these two points: (2, -3) and (2, 4).
SOLUTION
Use the distance formula and plug in the numbers to where they go. Since x1 = 2, y1 = -3, x2 = 2, and y2 = 4:
d = SQRT(2 - 2)2 + (4 + 3)2
The distance is = 7

Written Exercises
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You can do the following problems online. To do this you must either write down the problem you are doing and go to the programs page and select distance to enter your problem or you can click on this link Distance Program,-{if using Microsoft Internet Explorer it would be best to open the previous link in a separate window and then tile both these windows together}-, and move the frame spacer to the left to provide more room for the program. When you are done please click this link to return to the V.I.Geometry. Thank you, and Enjoy.

Find the distance between the following points.
 1.(3, 10) & (2, 1) 2.(-2, 0) & (5, 0) 3.(4, 3) & (6, -4) 4.(-10, 5) & (-10, -3) 5.(67, 32) & (47, 42) 6.(-3, 0) & (0, -4)