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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
