plotting, midpoint, distance, slope. cartesian plane coordinates are written in the following order

Cartesian PlanePlotting, Midpoint, Distance, Slope

Cartesian Plane

),( yx

Coordinates are written in the following order

Cartesian Plane),( yx

:A:B:C:D

Cartesian Plane),( yx

)3,4(:A

:B:C

:D

Cartesian Plane),( yx

)3,4(:A)0,2(:B

:C:D

Cartesian Plane),( yx

)3,4(:A)0,2(:B)2,3(: C

:D

Cartesian Plane),( yx

)3,4(:A)0,2(:B)2,3(: C)4,1(: D

Definition: Midpoint/DistanceMidpoint – The MIDPOINT of a segment is

the point halfway between the endpoints of the segment. May think of it as the coordinate the averages the x and the y.

Distance – The length from point A to point B. Note that the length from A to B is the same as the length from B to A

Definition: Midpoint/DistanceMidpoint – The MIDPOINT of a segment is

the point halfway between the endpoints of the segment. May think of it as the coordinate the averages the x and the y.

Distance – The length from point A to point B. Note that the length from A to B is the same as the length from B to A

2

,2

2121 yyxxM

Definition: Midpoint/DistanceMidpoint – The MIDPOINT of a segment is

the point halfway between the endpoints of the segment. May think of it as the coordinate the averages the x and the y.

Distance – The length from point A to point B. Note that the length from A to B is the same as the length from B to A

2

,2

2121 yyxxM

212

212 )()( yyxxD

Example: Midpoint

2

,2

2121 yyxxM

)2,2(:),8,4(: BA

x

y

Example: Midpoint

2

,2

2121 yyxxM

)2,2(:),8,4(: BA

x

y

2

28,

2

)2(4M

Example: Midpoint

2

,2

2121 yyxxM

)2,2(:),8,4(: BA

x

y

2

28,

2

)2(4M

2

10,2

2M

Example: Midpoint

2

,2

2121 yyxxM

)2,2(:),8,4(: BA

x

y

2

28,

2

)2(4M

2

10,2

2M )5,1(M

Example: Midpoint

2

,2

2121 yyxxM

)2,2(:),8,4(: BA

2

28,

2

)2(4M

2

10,2

2M )5,1(M

x

y

Distance2

122

12 )()( yyxxD )2,2(:),8,4(: BA

Distance2

122

12 )()( yyxxD )2,2(:),8,4(: BA

22 )28())2(4( D

Distance2

122

12 )()( yyxxD )2,2(:),8,4(: BA

22 )28())2(4( D22 )6()6( D

Distance2

122

12 )()( yyxxD )2,2(:),8,4(: BA

22 )28())2(4( D22 )6()6( D

3636D

Distance2

122

12 )()( yyxxD )2,2(:),8,4(: BA

22 )28())2(4( D22 )6()6( D

3636D

72D

Distance2

122

12 )()( yyxxD )2,2(:),8,4(: BA

22 )28())2(4( D22 )6()6( D

3636D

2672 D

x

y

SlopeThe SLOPE of a line is a number determined

by any two points on the line. This number describes how steep the line is. The greater the absolute value of the slope, the steeper the line.

SlopeThe SLOPE of a line is a number determined

by any two points on the line. This number describes how steep the line is. The greater the absolute value of the slope, the steeper the line.

12

12

xx

yy

x

y

run

risem

Slope

)2,2(:),8,4(: BA

x

y

12

12

xx

yy

x

y

run

risem

Slope

)2,2(:),8,4(: BA

x

y

12

12

xx

yy

x

y

run

risem

12

12

xx

yym

Slope

)2,2(:),8,4(: BA

x

y

12

12

xx

yy

x

y

run

risem

)2(4

28

12

12

xx

yym

Slope

)2,2(:),8,4(: BA

x

y

12

12

xx

yy

x

y

run

risem

6

6

)2(4

28

12

12

xx

yym

Slope

)2,2(:),8,4(: BA

x

y

12

12

xx

yy

x

y

run

risem

16

6

)2(4

28

12

12

xx

yym

HomeworkPlot the following sets of coordinate, each on

their own set of axis. Then, compute the midpoint, distance and slope between the following points. Once you have completed all 4 points describe the different types of slopes that you calculated. Example: Positive slope – the incline goes up as you go from left to right.

)5,2(:),3,2(:.1 BA )5,2(:),3,2(:.2 DC

)5,2(:),3,2(:.4 HG )2,3(:),2,5(:.3 FE