Section 3 - Calculations

This section shows the rules for finding the distance between geometric objects.

The distance between two points is always the length of a straight line between them.

The distance between a point and a line is always the length of a straight line from the point to the line and also being perpendicular to the first line.

The distance from a point to a plane is always the length of a line extending from the point to the plane, with the line being perpendicular to the plane.

One of the ways to find the distance between two points is using a number line. A number line makes it easy to find the distance between two points on the line. When a point is placed on the line, it is given a numerical value. This number is also called a coordinate. The distance between two points can be found be finding the positive difference of the points' coordinates. Number lines can also be used to find the coordinate of a line's midpoint.

Find the distance between A and B.

A = -7

B = 6

6 - (-7) = 13

The distance between A and B is 13.

Find the coordinate of the midpoint of segment AB.

A = -7

B = 6

(6 + (-7))/2 = -.5

-.5 is the coordinate for the midpoint of segment AB.

Practice! Practice! Practice!

Use this picture for questions 1 - 8.

Name the line segment whose length is the distance between the following points.

1) A and B

2) B and C

3) E and D

4) F and C

Name the segment that is the distance between each point and line.

5) A and DE

6) D and AB

7) G and CF

8) E and AB

Use this drawing for numbers 9 - 11

9) Z

10) Y

11) T

Find the distance between the points

12) E and A

13) F and B

14) E and D

15) C and B

16) F and A

Find the coordinate of the midpoint of each segment

17) FC

18) BD