Rational Numbers on the Coordinate Plane. 6.NS.C.6c

Transcription

1 Rational Numbers on the Coordinate Plane 6.NS.C.6c

2 Copy all slides into your composition notebook.

3 Lesson 14 Ordered Pairs Objective: I can use ordered pairs to locate points on the coordinate plane. Guiding Question: (Write your answer on the lines below.) Why does order matter when using ordered pairs to locate points on a coordinate plane?

4 Lesson 14 Ordered Pairs New Vocabulary Write each term on a sticky note using the Frayer Model Ordered Pair a set of numbers used to identify points EX: (2,3) First Coordinate the first number in an ordered pair Second Coordinate the second number in an ordered pair Coordinate Plane a plane formed when a horizontal number line intersects with a vertical number line.

5 Lesson 14 Ordered Pairs The Coordinate Plane

6 Lesson 14 Ordered Pairs More New Vocabulary

7 Lesson 14 Ordered Pair How to write an ordered pair: An ordered pair is written as (x, y) X represents the first number in the ordered pair it is called the x coordinate Y represents the second number in the ordered pair it is called the y coordinate How to use an ordered pair to find a point on a plane: Ordered pairs are like a set of directions; The first coordinate (x coordinate) tells you where to go in one direction The second coordinate (y coordinate) tells you where to go in the second direction. EX: To find point A (3,4): First move 3 units to the right on the x axis (or horizontal number line) Then move 4 units up on the y axis (or vertical number line)

8 Lesson 14 Ordered Pair 2 3

9 Lesson 14 Ordered Pair When locating a point on a plane, always start at the origin (0, 0), then move left or right on the x axis, last move up or down on the y axis.

10 Lesson 15 Locating Ordered Pairs on a Coordinate Plane Objective: I can find a point on a coordinate plane using ordered pairs of rational numbers Guiding Question: (Write your answer on the lines below.) If a point lies on the x axis or the y - axis, what must be true about its coordinates?

11 Lesson 15 Locating Ordered Pairs on a Coordinate Plane Remember from Lesson 14

12 Lesson 15 Locating Ordered Pairs on a Coordinate Plane Extending the Axes Beyond Zero

13 Lesson 15 Locating Ordered Pairs on a Coordinate Plane Points that lie on an axes Points that lie on the x axis have the following ordered pair: any number for the x coordinate and 0 for the y coordinate (any number, 0) EX: (2, 0) Points that lie on the y axis have the following ordered pair: 0 for the x coordinate and any number for the y coordinate. (0, any number) EX: (0, -4)

14 Lesson 15 Locating Ordered Pairs on a Coordinate Plane New Vocabulary Quadrants Quadrant I has all positive numbers EX:(5,4) Quadrant II: x is negative and y is positive EX: (-4, 3) Quadrant III has all negative numbers EX: (-3, -2) Quadrant IV: x is positive and y is negative EX: (2, -4)

15 Lesson 16 Symmetry in the Coordinate Plane Objective: I can use opposite numbers in ordered pairs to create reflections across axes. Guiding Question: (Write your answer on the lines below.) What is the relationship between (5, -1) and (5, 1)? How are they similar, how are they different?

16 Lesson 16 Symmetry in the Coordinate Plane New Vocabulary Symmetry and Reflection

17 Lesson 16 Symmetry in the Coordinate Plane Extending Opposites in the Coordinate Plane

18 Lesson 16 Symmetry in the Coordinate Plane Reflecting Points in the Coordinate Plane How to reflect a point across an axis: A point is reflected by creating another point that has an opposite x coordinate or y coordinate or both. To reflect the point S (5, 3) across the x axis, create a new point where the x coordinate is the same and the y coordinate is the opposite (5, -3) and give the new point a new name Point M. To reflect Point S ( 5, 3)across the y axis, create a new point where the x coordinate is the opposite and the y coordinate is the same (-5, 3) and give the new point a new name Point L.

19 Lesson 16 Symmetry in the Coordinate Plane Reflecting Points in the Coordinate Plane How to reflect a point across an axis: A point is reflected by creating another point that has an opposite x coordinate or y coordinate or both. To reflect the point S (5, 3) across both axes, create a new point where the x coordinate is the opposite and the y coordinate is the opposite (-5, -3) and give the new point a new name Point A.

20 Lesson 17 Drawing the Coordinate Plane and Points on the Coordinate Plane Objective: I can draw the coordinate plane including all parts and graph points on the coordinate plane. Guiding Question: (Write your answer on the lines below.) Why is it important to label the axes when setting up a coordinate plane?

21 Lesson 17 Drawing the Coordinate Plane and Points on the Coordinate Plane Quadrant I has all positive numbers EX:(5,4) The Coordinate Plane Quadrant II: x is negative and y is positive EX: (-4, 3) Ordered Pair Quadrant III has all negative numbers EX: (-3, -2) Quadrant IV: x is positive and y is negative EX: (2, -4) Point

22 Lesson 17 The Coordinate Plane When locating a point on a plane, always start at the origin (0, 0), then move left or right on the x axis, last move up or down on the y axis.

23 Lesson 18 Distance the Coordinate Plane Objective: I can compute the length of line segments with integer coordinates for end points in the coordinate plane by counting the number of units between end points and using absolute value. Guiding Question: (Write your answer on the lines below.) How do you find the length of a line segment using two ordered pairs?

24 Lesson 18 Distance the Coordinate Plane Finding the distance between two points by counting units. Point J (-5, 4) Point Z (-5, -6) Point J and Z will create straight vertical line when connected since both x coordinates are the same. Since the x coordinates are the same, count the units between the y coordinates. How many units are between 4 and -6? The are 10 units between 4 and -6. Therefore the distance between points J and Z is 10 units.

25 Lesson 18 Distance the Coordinate Plane Finding the distance between two points by using absolute value. Point J (-5, 4) Point Z (-5, -6) Point J and Z will create straight vertical line when connected since both x coordinates are the same. Since the x coordinates are the same, you can add the absolute values of the y coordinates. The absolute value of 4 is 4. The absolute value of -6 is 6 Add: = 10 Therefore the distance between points J and Z is 10 units.

26 Lesson 18 Distance the Coordinate Plane Finding the distance between two points by using absolute value. If two points have the same x coordinate or y coordinate you can use absolute value to find the distance between them. How to use absolute value: For integers that have opposite signs (one positive, one negative), add their absolute values. EX: (5, 4) and (5, -6) 4 is positive and 6 is negative The absolute value of 4 is 4. The absolute value of -6 is 6 Add: = 10, therefore, the distance between (5, 4) and (5, -6) is 10 units. For integers that have the same signs (both positive or both negative), subtract their absolute values. EX: (-8, 2) and (-5, 2): 8 is negative and 5 is negative The absolute value of -8 is 8. The absolute value of -5 is 5 Add: 8 5 = 3, therefore, the distance between (-8, 2) and (-5, 2) is 3 units.

27 Lesson 18 Distance the Coordinate Plane Completing the exercises using absolute value a. (-3, 4) and (-3, 9) 1. Cross out the coordinates that are the same. 2. Circle the coordinates that are different. 1. Are the signs the same? 1. If yes - subtract. 2. If no add 4 and 9 are both positive so we subtract their absolute values. 9 4 = 5, Therefore, the distance between (-3, 4) and (-3, 9) is 5.