2-4: THE COORDINATE PLANE

2-4: The Coordinate Plane

COORDINATE PLANE: A grid used to represent placement in two dimensions (x and y). Also called a CARTESIAN PLANE.

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

yVertical number lineis called the y-axis

Horizontal number lineis called the x-axis

The point of intersectionof the two axis is calledthe origin

2-4: The Coordinate Plane

The Coordinate plane is broken up into four quadrants. They start in the upper-right and count counter-clockwise.

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

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y

Quad 1Quad 2

Quad 4Quad 3

2-4: The Coordinate Plane

ORDERED PAIR: A point on the coordinate plane, consisting of an x-coordinate and a y-coordinate.

2-4: The Coordinate Plane

The figure below shows the graph of the ordered pair (4, 3). The first part, 4, is called the x-coordinate. It tells how many points to the left or right the point lies.

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

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–4

–5

y

(4, 3)

2-4: The Coordinate Plane

The second part, 3, is called the y-coordinate. It tells how many points up or down the point lies.

1 2 3 4 5–1–2–3–4–5 x

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3

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5

–1

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y

(4, 3)

2-4: The Coordinate Plane

Example: Graph point A at (2, -3)

Identify the coordinates at B and C.

1 2 3 4 5–1–2–3–4–5 x

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y

A (2,-3)

B

C

B is at (-2, 5); C is at (0, -2)

2-4: The Coordinate Plane

Horizontal and vertical lines have special characteristics. If a vertical line passes through (3, 4), then it contains all

the points where x = 3. If a horizontal line passes through (-4, -2), then it

contains all the points where y = -2.

THEOREM 2-4: If a and b are realnumbers, a vertical line containsall points (x, y) such thatx = a, and a horizontal linecontains all points (x, y) suchthat y = b.

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

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–5

y

2-4: The Coordinate Plane

THEOREM 2-4: If a and b are real numbers, a vertical line contains all points (x, y) such that x = a, and a horizontal line contains all points (x, y) such that y = b.

What??? Vertical lines are always written as x = # Horizontal lines are always written as y = # How am I supposed to remember that? Take a v (for vertical), and turn it upside-down Take a h (for horizontal), and turn it upside down

v h

2-4: The Coordinate Plane

Assignment Worksheet #2-4

Tomorrow Quiz on Sections 2-1 through 2-4

Next Week Monday: 2-5 (Midpoints) Tuesday: (Keystone Review-ish) Wednesday: Chapter 2 Preview Thursday: Chapter 2 Review Friday: Chapter 2 Test