Intro to coordinate plane
- 1. ( )2,4− ( )5,1 -5 -5 5 5 ( )2,2 −− ( )1,7 − y x
- 2. Imagine the top surface of your desk stretching in every direction. If it continued to spread , it would go right through your neighbor . . .
- 3. . . . and then through the classroom walls . . .
- 4. . . . and through the school and the hills and the mountains and out into space until it went on forever in every direction.
- 5. Then you would have a plane. In mathematics, a plane is a flat surface that goes on forever in every direction.
- 6. The coordinate plane is divided by two number lines. One is horizontal, like the number line you already know. -5 50 10-10
- 7. The other is vertical, with up being the positive direction and down being the negative direction.
- 8. Parts of a coordinate plane. Y- axis, is a vertical line. X – axis is a horizontal line. y x -5 50 10-10 5 -5
- 9. Coordinate Plane The number lines, when drawn like this, are called "axes”. The horizontal number line is called the "x-axis." The vertical one is the y- axis.The point at which they intersect, (0,0), is called the origin.
- 10. Parts of a coordinate plane. y x The coordinate plane is divided into 4 parts called quadrants. Quadrant IQuadrant II Quadrant III Quadrant IV
- 11. Coordinate Graphs The two axes divide the plane into four sections called “quadrants”. The quadrants are labeled with Roman Numerals, starting in the upper right corner and going counterclockwise.
- 12. The coordinate plane is filled with points . . .
- 13. . . . infinitely many points. And somewhere among all those points is the point we call the origin. I only know my way home from the origin!!!
- 14. y x -10 -5 5 10 An ordered pair is a set of coordinates, (x,y). The origin is located at (0,0) origin 5 10 -5 -10 means A Point !
- 15. X- axis Y-axis origin Quadrant I where both x and y are positive Quadrant II where x is negative and y is positive Quadrant III where both x and y are negative Quadrant IV where x is positive and y is negative Everything at a glance!
- 16. y x -10 -5 5 10 To graph the point (4,2), move 4 units to the right of the origin, and 2 units up. 5 10 -5 -10 Which quadrant is this point in? The 1st quadrant.
- 17. y x -10 -5 5 10 Graph the point (-3, -2) and give the correct quadrant. 5 10 -5 -10 (-3, -2) is in the 3rd quadrant.
- 18. y x -10 -5 5 10 Graph the point (-4,5 ) and give the correct quadrant. 5 10 -5 -10 (-4, 5) is in the 2nd quadrant.
- 19. y x -10 -5 5 10 Graph the point (3, -4) and give the correct quadrant. 5 10 -5 -10 (3, -4) is in the 4th quadrant.
- 20. “Whoa, Mrs. G.,What does this have to do with absolute value and equations? That’s what we learned this whole chapter!!!!!!!” So, glad you asked! More fun math coming your way!
- 21. Well, absolute value is what we use to find the distance from one point to another point in the coordinate plane! Watch, I’ll show you!
- 23. You guys are so smart!!!! But, I have a question for you. • What if point A is (-400,50) and point is B (600, 50)? • Remember, the coordinate plane goes to . Are you really going to be able to graph large numbered points on your paper and count? ∞
- 24. A (-400,50) To find the distance between these two points, we need to find the absolute value of the difference between the x –coordinates of each point. | -400-600|= |-1000| Difference B (600, 50)?
- 25. • -400 0 600 • All you need to do is take the absolute value of the difference of the x- coordinates of both points!!! • | -400-600|= |-1000| = 1000 units • Sure beats counting to 1000!! • That was easy!!
- 26. x y A B(-4,5) (6,5) 0 |-4-6|= Difference |-10|= 10 units
- 27. Name the coordinates of the plotted points. Find the perimeter and area of the figure. x y A B D C A ______ B ______ C ______ D ______ (-2, 2) (5, 2) (5, -3) (-2, -3) Length Width
- 28. x y A B D C Absolute value of the difference in the x-coordinates Length = = |-2-5| = A(-2, 2) B(5, 2) 7
- 29. x y A B D C The absolute value of difference in the y-coordinates Length = Width = |-2-5| = 7 = |2-(-3)| = 5 A(-2, 2) D(-2, -3)
- 30. A B D C Perimeter = 5 + 5 + 7 + 7 = 24 units Area = 5 7• = 35un2 Width=5 Length=7