Mr. Britten’s Math Class The Coordinate Plane

The Coordinate Plane -5 5

Imagine the top surface of your desk stretching in every direction. If it continued to spread , it would go right through your neighbor . . . . . . and then through the classroom walls . . .

Then you would have a plane. . . . and through the school and the hills and the mountains and out into space until it went on forever in every direction. Then you would have a plane.

In Math, we often use the coordinate plane. In mathematics, a plane is a flat surface that goes on forever in every direction. In Math, we often use the coordinate plane.

The coordinate plane is divided by two number lines The coordinate plane is divided by two number lines. One is horizontal, like the number line you already know. -5 5 10 -10

The other is vertical, with up being the positive direction and down being the negative direction.

-5 5 10 -10

The coordinate plane is filled with points . . .

. . . infinitely many points. And somewhere among all those points is the point we call the origin. lemniscate The infinity symbol ∞ (sometimes called the lemniscate) is a mathematical symbol representing the concept of infinity.

The origin is the point where the two number lines meet. -5 5 10 -10 The origin is the point where the two number lines meet.

The two number lines have special names. -5 5 10 -10 The two number lines have special names. The horizontal number line is called the x-axis. The vertical number line is called the y-axis.

The plural of axis is axes. We often talk about the coordinate axes. -5 5 10 -10 The plural of axis is axes. We often talk about the coordinate axes.

To study a point, we need to know where to find it To study a point, we need to know where to find it. So we give it coordinates. Coordinates are like an address. They tell you how you can get to a point if you start at the origin.

Coordinates are always written in parentheses, with the x-value first. -5 5 10 -10 Coordinates are always written in parentheses, with the x-value first.

Coordinates written in parentheses are called an ordered pair. -5 5 10 -10 Coordinates written in parentheses are called an ordered pair.

Consider the point which has coordinates, (4, -2). -5 5 10 -10 Consider the point which has coordinates, (4, -2). So the 4 in (4, -2) says we need to move 4 units to the right. The first number tells you how far to move along the x-axis. Remember to start at the origin!

The second number tells you how far to move up or down. -5 5 10 -10 The second number tells you how far to move up or down. The –2 in (4, -2) tells you to move down two units.

To get to the origin from the origin, we don’t move at all. -5 5 10 -10 To get to the origin from the origin, we don’t move at all. So the origin is designated by the ordered pair, (0, 0)

In Quadrant II, x-values are negative, while y-values are positive. -5 5 10 -10 In Quadrant II, x-values are negative, while y-values are positive. In Quadrant I, all values are positive. The two number lines divide the plane into four regions. With Roman Numerals. We call the regions quadrants. In Quadrant IV, x-values are positive and y-values are negative. In Quadrant III, x- and y-values are both negative.

Give the coordinates of each point:

Plot each point and describe how to get to the point from the origin. From the origin, move to the right 8 units, then down 7 units. (8,–7) (4,0) (–4,–5) (0,–9) (7,12) From the origin, move to the right 4 units, then stop (Stay on the x-axis.). From the origin, move to the left 4 units, then down 5 units. From the origin, don’t move to the right or left (stay on the y-axis), then move down 9 units. From the origin, move to the right 7 units, then up 12 units.

Use your own words to explain what each term means: Origin Quadrant Axis Coordinates Ordered pair

Mr. Britten’s Math Class Advanced Math due 11/19/2018 Name: __________________ 1. A coordinate system, or coordinate plane, is used to locate points in a 2-dimensional plane. The horizontal number line is the _____________ and the vertical number line is the ____________ and their intersection is the ____________. (Choose from: Origin, X-axis or Y-axis). 2. Label the four quadrants in the coordinate plane below. Also label the origin O. Graph the point (2, 8) on the coordinate plane as well. Hint: Use your notes you took in class. 3. True or false? The ordered pair (48, 107) has Y-coordinate 48 and X-coordinate 107. _________________ 4. True or false? The ordered pair (19, 88) has Y-Coordinate 88 and X-coordinate 19. __________________ 5. Graph the following points in the graph below. A). (3, -2), (2, 3), (-5, 5), (-7, 8), (-5, 0).

Mr. Britten’s Math Class Advanced Math due 11/19/2018 Name: __________________ 6. Write the ordered pair for each given point. E ______ M______ P______ G_______ Q______ N______ 7. Identify the quadrant containing each point. Choose: I, II, III, IV B – Quadrant ____ J – Quadrant ____ I – Quadrant ____ D – Quadrant ____ E – Quadrant ____ 8. Name the ordered pair for each point on the city map below. Hint: (x,y) A). City Hall _________________ B). Theater __________________ C). Gas Station _______________ D). Grocery __________________

Mr. Britten’s Math Class Adv Mr. Britten’s Math Class Adv. Math Pop Qz 11/15/18 Name: _______________ 1. Usain Bolt is considered the fastest man in the world since 2009. His record was a top speed of 28 miles per hour (rounding off*). The top speed of a cheetah is 75 miles per hour. What is the percentage of Usain Bolt’s top speed to the cheetah’s top speed? Show your work to receive full credit! *The actual value of Usain Bolt’s speed was 27.8 mph. Bonus points: Calculate the percentage above using this new number for extra credit. \m/

Mr. Britten’s Math Class Reg Mr. Britten’s Math Class Reg. Math Pop Qz 11/15/18 Name: _______________ 1. Usain Bolt is considered the fastest man in the world since 2009. His record was a top speed of 28 miles per hour (rounding off*). The top speed of a cheetah is 75 miles per hour. What is the percentage of Usain Bolt’s top speed to the cheetah’s top speed? Show your work to receive full credit! *The actual value of Usain Bolt’s speed was 27.8 mph. Bonus points: Calculate the percentage above using this new number for extra credit. \m/