The Coordinate Plane 1.10 p. 50 Learn to locate and graph points on the coordinate plane, name the...

The Coordinate Plane

1.10 p. 50

Learn to locate and graph points on the coordinate plane, name the coordinates of points, and identify the quadrants.

The objectives in this lesson will be used as we graph linear functions and solve systems of equations. Please learn the terms that are used as we practice the skills.

Vocabularycoordinate planeaxesx-axisy-axisquadrantsoriginordered pairx-coordinatey-coordinate

These definitions will be coveredthroughout the lesson. We willreview them at the end of class.

A coordinate plane is formed by two number lines in a plane that intersect at right angles. The point of intersection is the zero on each number line.

• The two number lines are called the axes.

• Use this diagram to complete thelabels on the coordinate plane inyour notes.

• Each section of the diagram will bediscussed during the next few slides.

• The horizontal axis is called the x-axis.

• The vertical axis is called the y-axis.

• The two axes divide the coordinate plane into four quadrants.

• Please notice that Roman numerals areused to label thequadrants.

• The point where the axes intersect is called the origin.

• Its coordinates are(0,0)

An ordered pair gives the location of a point on a coordinate plane. The first number tells how far to move right (positive) or left (negative) from the origin. The second number tells how far to move up (positive) or down (negative).

The numbers in an ordered pair are called coordinates. The first number is called the x-coordinate. The second number is called the y-coordinate.

The ordered pair for the origin is (0,0).

Identifying Quadrants

Name the quadrant where each point is located.

A. X

B. Y

C. S

D.V

Quadrant IV

Quadrant III

Quadrant II

Quadrant I

What about point Z?

Points on the axes are not in any quadrant.Helpful Hint

Locating Points on a Coordinate Plane

Give the coordinates of each point.

A. X

From the origin, X is 4 units right and 1 unit down.

(4, –1)

B. Y

From the origin, Y is 2 units left, and 3 units down.

(–2, –3)

Locating Points on a Coordinate Plane

Give the coordinates of each point.

C. S

From the origin, S is 3 units left, and 3 units up.

(–3, 3)

D. V

From the origin, V is 4 units right and 2 units up. (4, 2)

E. Z

(0, 4)

From the origin, Z is 0 units right, and 4 units up.

C. T

From the origin, T is 1 unit right, and 3 units down.

(1, –3)

Points that are located on an axis may cause confusion. Look alongthe x-axis……..where do you have to stop to align with the point???

A positive x-value moves us to the right.A negative x-value moves us to the left.

A positive y-value moves us up.

A negative y-value moves us down.

( , )x y

x

y

( , )x y( , )+ + ( , )

( , )- + ( , )

( , )x y

( , )- - ( , )

( , )+ - ( , )

Quadrant??

I

II

III

IV

Let’s go back to the first page of your notes and put these signs in the appropriatequadrant.

x

y ( + , + )( - , + )

( - , - ) ( + , - )

Learn to associate the (x,y) signs with the quadrant.

Now let’s graph…...

Graphing Points on a Coordinate Plane

Graph each point on a coordinate plane.

M(4, 3)

Q (–4, 1)

x

y

–4 –2 0 2 4

4

2

–2

–4

From the origin, move 4 units right, and 3 units up.

M

QFrom the origin, move 4 units left, and 1 unit up.

From the origin, move 3 units down.

R (0, -3)R.

Graph each point on a coordinate plane.

L(3, 4)

N (–3, –3)

x

y

–4 –2 0 2 4

4

2

–2

–4

From the origin, move 3 units right, and 4 units up.

L

N

From the origin, move 3 units left, and 3 units down.

P

P (1, –2)

From the origin, move 1 unit right and 2 units down.

Lesson QuizName the quadrant where each ordered pair is located.

1. (3, –5) 2. (–4, –2)

3. (6, 2) 4. (–7, 9)

Give the coordinates of each point.

5. A 6. B

7. C 8. D

IIIIV

I II

(–2, 3) (1, 2)

(0, –2) (–2, –3)

x

y

Graph these points

A (4, 0) E ( -3, 5)

B(-2, -2) F( 3, -4)

C (0, -5) G (0, 0)

D(4, 4) H ( -4, 2)

A

H

G

F

E

D

C

B

What have we accomplished?

• We have graphed locations on the coordinate plane using ordered pairs (coordinates).

• We have identified the regions on the plane as quadrants.

• We have used coordinates to identify points.