CIRCUMFERENCEEXAMPLECIRCUMFERENCE IS THE MEASURE OF THE DISTANCEGRA...

5. CircumferenceExampleCircumference is the measure of the distanceGraph the following points: (2,3), (3,−2), (−2,3),around the outside of a circle.and (−3,−2).II I

Circumference

(−2,3) (2,3)(−3,−2) (3,−2)III IVNotice that the graph is broken up into fourquadrants with one point plotted in each one.

–

M E A S U R E M E N T A N D G E O M E T R Y

–

This chart indicates which quadrants contain whichordered pairs based on their signs:Find the midpoint of line segment AB.

B

Sign of

(5,10)

Points Coordinates Quadrant (2,3) (+,+) I (–2,3) (–,+) II (–3,–2) (–,–) III

Midpoint

(3,–2) (+,–) IVLengths of Horizontal and VerticalSegments

(1,2)

Two points with the same y-coordinate lie on the

A

same horizontal line and two points with the same x-coordinate lie on the same vertical line. The length ofa horizontal or vertical segment can be found by takingthe absolute value of the difference of the two points orSolution:by counting the spaces on the graph between them.

5

=

6

Midpoint x=

1 +

2

2

= 32

= 60

=

1

Midpoint y= 2 +

1

Find the lengths ofABand line BC.Therefore the midpoint ofABis (3,6).(7,5) C(2,1)BA| 2 −7 | = 5 = AB| 1 −5 | = 4 = BCMidpointTo find the midpoint of a segment, use the following for-mula:

x

2

y

2

Midpoint y=

y

1

+

Midpoint x=

x

1

+

4 0 3

Slope

I

^MPORTANT

I

NFORMATION ABOUT

S

^LOPE

■

A line that rises from left to right has a positiveThe slope of a line measures its steepness. It is found slope and a line that falls from left to right has aby writing the change in the y-coordinates of any twonegative slope.points on the line, over the change of the correspondingx-coordinates. (This is also known as the rise over the

■

A horizontal line has a slope of 0, and a verticalline does not have a slope at all—it is undefined.run.) The last step is to simplify the fraction that results.

■

Parallel lines have equal slopes.

■

Perpendicular lines have slopes that are negativereciprocals.Find the slope of a line containing the points (3,2) and (8,9).(8,9)(3,2)

9

−

2

5

3

=

7

8

−

Therefore, the slope of the line is

7