COORDINATE GEOMETRY For example: Main Street runs from A2 to H2, and the City Middle School can be found at G5. In some towns, streets are laid out in.

COORDINATE GEOMETRY For example: Main Street runs from A2 to H2, and the City Middle School can be found at G5. In some towns, streets are laid out in a grid and it is very easy to tell someone how to get from one place to another.

The Cartesian Coordinate System
is similar to a town grid. A coordinate grid is a way to locate points in a plane. Y It is formed by the intersection of a horizontal number line, called the x-axis, and a vertical number line, called the y-axis. X Origin (0,0) These axes intersect at a point called the origin (0,0). Historical link

Rene Descartes was a 17th century philosopher and mathematician.
The story goes that he was gazing upward, deep in thought, when he saw a fly walking on the ceiling. It occurred to Descartes that the fly’s position on the ceiling could always be described by two numbers: its distance from each of two walls. Thus was born the coordinate plane, also called the Cartesian coordinate system after Descartes.

Goals of the lesson Identify Ordered Pairs in the Coordinate Plane.
Graph Ordered Pairs in the Coordinate Plane. Describe Ordered Pairs in the four quadrants of the Coordinate Plane.

Ordered Pairs You can name any point on the plane with 2 numbers (called coordinates). X Y (4,5) The FIRST number is for the distance from the origin along the x-axis, the x-coordinate. 5 units The SECOND number is for the distance along the y-axis, the y-coordinate. 4 units Since the pair is ALWAYS named in order (first x, then y), it’s called an ordered pair (x,y).

Quadrants The x- and y-axes divide the plane into four regions called quadrants, numbered I, II, III, and IV. X Y II I (-X,+Y) (+X,+Y) Notice the type of ordered pairs in each quadrant. III IV (-X,-Y) (+X,-Y)

X Y What ordered pair is the bumble bee pointing at? (Hint: start at the origin and count how far the point is along the x-axis, then count how far the point is along the y-axis.) (5,3) (3,5) (-3,5)

Bummer dude! Remember: The order is important.
X Y Remember: The order is important. The x-coordinate is first. (-5, 3) Followed by the y-coordinate. And just like the order in the alphabet: x followed by y gives you (x,y). TRY AGAIN

Hmmm…… Remember: negative positive
A positive x-coordinate is to the right of the origin, X and a negative x-coordinate is to the left of the origin. A positive y-coordinate goes up from the origin, positive and a negative y-coordinate goes down from the origin. negative TRY AGAIN Y

Let’s try another one. X Y (1,3) (3,1)

SWEET! Looks like you understand!
X Y Let’s try another one. (5,1) (5,-1) (1,5)

Right on! Now let’s try some points in the other quadrants.
X Y Right on! Now let’s try some points in the other quadrants. (3,-4) (-4,3) (-4,-3)

Well done! You are on the ball! Just a few more to go.
X Y Well done! You are on the ball! Just a few more to go. (4,0) (0,-4) (-4,0)

REMEMBER: X Y All of the points along the X-axis have a Y-value equal to ZERO. II I For example: (-7,0), III IV (-2,0), And (3,0) are all points ON the X-axis. TRY AGAIN

“Bee”eautiful! Keep up the good work!
X Y “Bee”eautiful! Keep up the good work! (-7,-7) (7,-7) (-7,7)

Right on again! Just two more to go and we are moving on.
X Y Right on again! Just two more to go and we are moving on. (0,6) (-6,0) (0,-6)

REMEMBER: X Y All of the points along the Y-axis have a X-value equal to ZERO. II I For example: (0,5), (0,-1), III IV And (0,-6) are all points ON the Y-axis. TRY AGAIN

You are really buzzing now!
X Y (6,3) (6,-3) (-3,6)

II II I I III IV III IV THE QUADRANTS
Now let’s look at what type of ordered pairs are in each quadrant by having you answer some questions. X Y II II I I All the points in the first quadrant are: Positive X’s & Negative Y’s Positive X’s & Positive Y’s III IV III IV Negative X’s & Negative Y’s Negative X’s & Positive Y’s

All the points in the second quadrant are:
THE QUADRANTS Rock on!! X Y All the points in the second quadrant are: II I Positive X’s & Negative Y’s Positive X’s & Positive Y’s III IV Negative X’s & Negative Y’s Negative X’s & Positive Y’s

All the points in the third quadrant are:
“Bee”rilliant!! THE QUADRANTS X Y All the points in the third quadrant are: II I Positive X’s & Negative Y’s Positive X’s & Positive Y’s III IV Negative X’s & Negative Y’s Negative X’s & Positive Y’s

All the points in the fourth quadrant are:
THE QUADRANTS Simply Smashing! X Y All the points in the fourth quadrant are: II I Positive X’s & Negative Y’s Positive X’s & Positive Y’s III IV Negative X’s & Negative Y’s Negative X’s & Positive Y’s

All the points along the x-axis have:
THE QUADRANTS You got in going on! X Y All the points along the x-axis have: II I Y equaling zero X equaling zero III IV

REMEMBER: X Y All of the points along the X-axis have a Y-value equal to ZERO. II I For example: (-7,0), III IV (-2,0), And (3,0) are all points ON the X-axis. TRY AGAIN

All the points along the y-axis have:
You “Bee” long in an advanced math class! THE QUADRANTS X Y All the points along the y-axis have: II I Y equaling zero X equaling zero III IV

REMEMBER: X Y All of the points along the Y-axis have a X-value equal to ZERO. II I For example: (0,5), (0,-1), III IV And (0,-6) are all points ON the Y-axis. TRY AGAIN

Sweet as honey! It looks like you are ready for a challenging game for your tutorial assessment! The game is called Maze Game and the screen looks like this. The object of the game is to get the character to the green dot without hitting a mine. You will do this by using your knowledge of the coordinate plane and ordered pairs. next

You will need a piece of paper to record the following:
1) Number of mines you choose. 2) The list of the ordered pairs you used to finish the maze successfully. 3) A record of any errors you made along the way, and what you learned from them. You will turn this in at the end of the lesson. You are to play until you complete the maze once or for a maximum of 10 minutes. When you finish close your web browser and open power point again. Press here to play Click here after you finish

CONGRATULATIONS! You have completed your introductory lesson on Coordinate Geometry!!!!!!! Don’t forget to turn you paper into Mr. Kerlin Click here to return to the start

COORDINATE GEOMETRY For example: Main Street runs from A2 to H2, and the City Middle School can be found at G5. In some towns, streets are laid out in.

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COORDINATE GEOMETRY For example: Main Street runs from A2 to H2, and the City Middle School can be found at G5. In some towns, streets are laid out in.

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Presentation on theme: "COORDINATE GEOMETRY For example: Main Street runs from A2 to H2, and the City Middle School can be found at G5. In some towns, streets are laid out in."— Presentation transcript:

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