You will learn to name and graph ordered
pairs on acoordinate plane.
In coordinate geometry, grid paper is used to
locate points.
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
You will learn to find the distance of a line
segment.
The distance of a line segment AB is found by the formula
BA
d (x2 x1)2 (y2 y1)
2
You will learn to find the coordinates of the
midpoint of a segment.
bisectsThe midpoint of a line segment AB
is the point C that ______ the segment.
BA C
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
The horizontal number lineis called the ______.x-axis
The vertical number lineis called the ______.y-axis
O
Quadrant I(+, +)
Quadrant II
(–, +)
Quadrant III
(–, –)
Quadrant IV
(+, –)
Lets’ lookat thegrid.
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
O
The point of intersection of the twoaxes is called the _____.origin
The two axes separate the plane intofour regions called _________.quadrants
Quadrant I(+, +)
Quadrant II
(–, +)
Quadrant III
(–, –)
Quadrant IV
(+, –)
Lets’ lookat thegrid.
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Point A(x, y) =
Point B(x, y) =
Point C(x, y) =
Point D(x, y) =
A
(3, 2)
(–3, 2) B
(–3, –2)C (3, –2)D
(3, 2)A
DC
B
(–3, –2)
(–3, 2) (3, –2)
Now, see if you can name the
points.
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
A(2, 4)B(2, 0)C(2, –3)D(2, –5)
On a piece of grid paper draw lines
representing the x-axis and the y-axis.
Graph :
OK, It’s your turn
A
B
C
D
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Consider these questions:
What do you notice about the graphs of
these points?
They lie on a vertical
line.
OK, It’s your turn
A
B
C
D
x = 2
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Consider these questions:
What do you notice about the x-coordinates
of these points?
They are the same
number.
OK, It’s your turn
A
B
C
D
A(2, 4)B(2, 0)C(2, –3)D(2, –5)
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Consider these questions:
Write a general statement about ordered pairs that
have the same x-coordinate.
They lie on a vertical line
that intersects the x-axis at
the x-coordinate.
OK, It’s your turn
A
B
C
D
d (x2 x1)2 (y2 y1)
2
Find the distance between two points.
(-2,5) and (8,3)
d (8 2)2 (3 5)2
d=10.19803903
How about thedistance between
two points
Find the midpoint between two
points.
(0.45,7) and (-0.3,-9)
(0.075,-1)
x2 x1
2,y2 y1
2
0.3 0.45
2, 9 7
2
Lets’ look at finding a midpoint.
0
y
0 x
10-1 2 4 6 8 10
10
-1
2
4
6
8
10
-2 3 7-2
1
5
9
1 9
3
-2-2
5
7
Find the midpoint, C(x, y), of a segment on the coordinate plane.
x = 1 x = 9
y = 7
y = 3
A(1, 7)
B(9, 3)
x
yC(5, 5)
0
y
0 x
10-1 2 4 6 8 10
10
-1
2
4
6
8
10
-2 3 7-2
1
5
9
1 9
3
-2-2
5
7
Graph A(1, 1) and B(7, 9)
C
Draw AB
B(7, 9)
A(1, 1)
Find the midpointof AB.
C(4, 5)
x-coordinate of B y-coordinate of B
Replace x1 with 7and y1 with 2
Multiply each side by 2
Add or subtract toisolate the variable
A(7, 2)
B(x, y) is somewhere over there.
B(-1, 8)
midpoint
C(3, 5)
Suppose C(3, 5) is the midpointof AB. Find the coordinate of B.
5x - 6 2x
CBA
Since B is the midpoint: AB = BC
Write the equation involving x: 5x – 6 = 2x
Solve for x: 5x – 2x – 6 = 2x – 2x
3x – 6 + 6 = 0 + 6
3x = 6
x = 2
AB = 5x – 6 = 5(2) – 6 = 10 – 6 = 4
BC = 2x = 2(2) = 4
Check!
In the figure, B is the midpoint of AC.
Find the value of x.
6. DF is bisected at point E, and DF = 8. What do you know about the lengths of DE and EF ?
7. In the figure below, R is the midpoint of QS. Find the value of d.
8. True or False: If AB CD, then CD AB.
9. True or False: If AB BC, then B is the midpoint of AC.
1.8 The Coordinate PlanGeometry
1. Name the coordinates of each point.
2. Graph point C at (0, –4).
4. Graph y = 2.
3. Graph x = –4.
5. Graph and label the intersection of x = –4 and y = 2
0
y
x
5-1 2 4
4
0
-2 1-3
2
3-2
-2
A
B
10. Find the distance: (-4,9),(1,-3)
11. Find the midpoint: (9,-2),(12,-14)
d + 4 3d
SRQ
6. DF is bisected at point E, and DF = 8. What do you know about the lengths of DE and EF ?
7. In the figure below, R is the midpoint of QS. Find the value of d.
8. True or False: If AB CD, then CD AB.
9. True or False: If AB BC, then B is the midpoint of AC.
1.8 The Coordinate PlanGeometry
1. Name the coordinates of each point.
A = (2, 0)
B = (3, –2)
2. Graph point C at (0, –4).
4. Graph y = 2.
3. Graph x = –4.
5. Graph and label the intersection of x = –4 and y = 2
0
y
x
5-1 2 4
4
0
-2 1-3
2
3-2
-2
A
B
10. Find the distance: (-4,9),(1,-3)
11. Find the midpoint: (9,-2),(12,-14)
d + 4 3d
SRQ
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