Coordinates and Design.  What numbers would you write on this line?  Each space is 1 unit 0.

Slides:



Advertisements
Similar presentations
Learn to recognize, describe, and show transformations.
Advertisements

Translations I can: Vocabulary: Define and identify translations.
TRANSFORMATIONS.
Jeopardy Opening.
(7.7) Geometry and spatial reasoning The student uses coordinate geometry to describe location on a plane. The student is expected to: (B) graph reflections.
Copyright Notice A Homemade PowerPoint Game by Sarah Grabowski University of Georgia Let’s Play Directions Story Credits Preparation Visible Game Board.
Unit 4: Linear Relations Unit 4: Linear Relations.
EQ: How can you investigate transformations? Lesson 13-5b Transformations pp Vocabulary to watch out for this lesson: Transformation Translation.
Transformations Dilations Translations Reflections Rotations.
Transformations 3-6, 3-7, & 3-8.
Coordinates and Design
Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.
Translations, Reflections, and Rotations
To transform something is to change it. In geometry, there are specific ways to describe how a figure is changed. The transformations you will learn about.
Holt CA Course 1 8-7Transformations Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview.
Chapter 7 Transformations.
Chapter 7 Transformations. Chapter Objectives Identify different types of transformations Define isometry Identify reflection and its characteristics.
In mathematics, a transformation
Chapter 7 Transformations. Examples of symmetry Lines of Symmetry.
Transformation in Geometry Transformation A transformation changes the position or size of a shape on a coordinate plane.
4.8 – Perform Congruence Transformations
8-10 Translations, Reflections, and Rotations Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation.
8-10 Translations, Reflections, and Rotations Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation.
Reflections Grade 6 Copyright © Ed2Net Learning Inc.1.
Coordinate Grids Ms. Cuervo.
E9 Students are expected to make generalizations about the properties of translations and reflections and apply these properties. E10 Students are expected.
GEOMETRY OUTCOME 1 CHAPTER 1 AND 3, WITH ADDED COMPONENTS.
Transformations 7-7 Properties of Transformations. Goal: By the end of the week, I will recognize the difference between translations, reflections, and.
Unit 1: Transformations, Congruence, and Similarity.
Copyright © Ed2Net Learning Inc.1. 2 G (4, -1) F (-1, 0) A (-5, 5) P (-4, -1) M (0, 5) B (-5, -3) Warm Up.
11-19 S 6.7: Perform Similarity Transformations. Review: Transformations: when a geometric figure is moved or changed in some way to produce a new figure.
9-2 Reflections Objective: To find reflection images of figures.
Copyright © Ed2Net Learning Inc.1. 2 Warm Up x y y = 3x - 11) x y y = x - 62)
Coordinates and Design. What You Will Learn: To use ordered pairs to plot points on a Cartesian plane To draw designs on a Cartesian plane To identify.
In the last several lessons, you have described translations using coordinates. You have also developed strategies for determining where an object started.
5.7 Reflections and Symmetry. Objective Identify and use reflections and lines of symmetry.
Chapter Transformations Part 1. Objective: Use a translation, a reflection, and a rotation Describe the image resulting from a transformation.
TRANSFORMATIONS. DEFINITION  A TRANSFORMATION is a change in a figure’s position or size.  An Image is the resulting figure of a translation, rotation,
Translations, Reflections, and Rotations. Vocabulary Transformation- changes the position or orientation of a figure. Image- the resulting figure after.
Graphing & Describing “Reflections”. We have learned that there are 4 types of transformations: 1)Translations 2)Reflections 3)Rotations 4)Dilations The.
Coordinate Planes and Transformations. Points on the Coordinate Plane The coordinate plane is made up of two number lines that intersect at right angles.
Transformation in Geometry Transformation A transformation changes the position or size of a polygon on a coordinate plane.
Translation Symmetry (Sliding).
Learning Objectives To draw transformations of reflections, rotations, translations and combinations of these using graph paper, transparencies, and.
Transformations.
A Homemade PowerPoint Game by Sarah Grabowski University of Georgia
3B Reflections 9-2 in textbook
Preview Warm Up California Standards Lesson Presentation.
Math 8 Learning Target: I can describe what transformations are and identify the different types.
A Homemade PowerPoint Game by Sarah Grabowski University of Georgia
Graphing & Describing “Reflections”
A movement of a figure in a plane.
A movement of a figure in a plane.
A movement of a figure in a plane.
A movement of a figure in a plane.
Transformations Day 1 Notes Slideshow.
The Ultimate PowerPoint Game
A Homemade PowerPoint Game by Sarah Grabowski University of Georgia
A Homemade PowerPoint Game by Sarah Grabowski University of Georgia
Transformations.
Math 8 Day 6 Learning Target: Students can describe what transformations are and identify the different types.
Transformations Dilations Translations Reflections Rotations.
Math 8 Learning Target: I can describe what transformations are and identify the different types.
A Homemade PowerPoint Game by Sarah Grabowski University of Georgia
A Homemade PowerPoint Game by Sarah Grabowski University of Georgia
A Homemade PowerPoint Game by Sarah Grabowski University of Georgia
Math 8 Learning Target: I can describe what transformations are and identify the different types.
Presentation transcript:

Coordinates and Design

 What numbers would you write on this line?  Each space is 1 unit 0

 What numbers would you write on this line?  Each space is 1 unit 0

 The Cartesian Plane (or coordinate grid) is made up of two number lines that intersect perpendicularly at their respective zero points. ORIGIN The point where the x-axis and the y-axis cross (0,0)

 The horizontal axis is called the x-axis.  The vertical axis is called the y-axis.

 The Coordinate Grid is made up of 4 Quadrants. QUADRANT IQUADRANT II QUADRANT IIIQUADRANT IV

 The signs of the quadrants are either positive (+) or negative (-). QUADRANT IQUADRANT II QUADRANT IIIQUADRANT IV (+, +) (-, +) (-, -)(+, -)

 Identify Points on a Coordinate Grid A: (x, y) B: (x, y) C: (x, y) D: (x, y) HINT: To find the X coordinate count how many units to the right if positive, or how many units to the left if negative.

.. 1.1 The Cartesian Plane Student Outcome: Identify and plot points in the 4 quadrants of the Cartesian plan using ordered pairs Identify Points on a Coordinate Grid A: (5, 7) B: (5, 3) C: (9, 3) D: (9, 7)

When we read coordinates we read them in the order x then y Plot the following points on the smart board A: (9, -2) B: (7, -5) C: (2, -4) D: (2, -1) E: (0, 1) F: (-2, 3) G: (-7, 4)

1. Units not the same in terms of intervals 2. Switch the order that they appear 3. Wrong symbols for quadrants

Textbook: Page 9 #5, 7, for questions 9 and 10 plot on two separate graphs. Graph paper is provided for you. Challenge #14, 16

 Put your thinking cap on! What is the following question asking us to find?  Label each vertex of each shape. Question! What is a vertex?

AB C A vertex is a point where two sides of a figure meet. The plural is vertices! The vertices of the Triangle are A (x, y) B (x, y) C (x, y) A (4, 4) B (0, 4) C (2, 0)

 Graphic Artists use coordinate grids to help them make certain designs. Flags, corporate logos can all be constructed through the use of our coordinate grids.

 Study the following Flag.  How many vertices can you find in the design.  Imagine seeing this on a coordinate grid.  Notice how it is centered and equally distributed on each side.

 Assignment:  You have been hired to create a flag for the company “Flags R Us!” They are looking for a new creative design that can be based on an interest or hobby of yours. The flag design can be a cool pattern or related to any sport, hobby, or activity you are involved with.  The flag needs to have a minimum of 10 Vertices.  They want a detailed location of any 10 vertices located on the bottom of your design (list the coordinates).  It is your responsibility to use a coordinate grid to create your own pattern.

 Your Flag will be evaluated as following” ◦ Neatness: (Have you made sure to color inside the lines). ◦ Vertices: (Do you have at least 10). ◦ Design : (Have you used designs and shapes to create an image). ◦ Handout : (Do you have all the vertices clearly labeled in a legend).

Student Name: 10 Vertices A)D)G)J) B)E)H) C)F)I)

 BLM 1-3, BLM 1-4, BLM 1-5, BLM 1-6

This section will focus on the use of Translations, Reflections, Rotations, and describe the image resulting from a transformation.

 Transformations: ◦ Include translations, reflections, and rotations.  Translation ReflectionRotation

 Translations are SLIDES!!! Let's examine some translations related to coordinate geometry.

 Translation: ◦ A slide along a straight line Count the number of horizontal units and vertical units represented by the translation arrow. The horizontal distance is 8 units to the right, and the vertical distance is 2 units down (+8 -2)

 Translation: ◦ Count the number of horizontal units the image has shifted. ◦ Count the number of vertical units the image has shifted. We would say the Transformation is: 1 unit left,6 units up or (-1+,6)

In this example we have moved each vertex 6 units along a straight line. If you have noticed the corresponding A is now labeled A’ What about the other letters?

A translation "slides" an object a fixed distance in a given direction. The original object and its translation have the same shape and size, and they face in the same direction

When you are sliding down a water slide, you are experiencing a translation. Your body is moving a given distance (the length of the slide) in a given direction. You do not change your size, shape or the direction in which you are facing.

 Let’s Practice  Textbook Page 25 ◦ Question #4a, b, 5,

 4 a) What is the translation shown in this picture? 6 units right, 5 units up Or (+6,+5)

 4 b) What is the translation in the diagram below? Horizontal Distance is: 6 units left Vertical Distance is: 4 units up Or (-6,+4)

 #5  B) The coordinates of the  translation image are ◦ P'(+7, +4), Q’(+7, –2), ◦ R'(+6, +1), S'(+5, +2).  C) The translation arrow is shown: 3 units right and 6 units down. (+3, -6)

 Is figure A’B’C’D’ a reflection image of figure ABCD in the line of reflection, n?  How do you know?  Figure A'B'C'D' IS a reflection image of figure ABCD in the line of reflection, n. Each vertex in the red figure is the same distance from the line of reflection, n, as its reflected vertex in the blue image.

A reflection is often called a flip. Under a reflection, the figure does not change size. It is simply flipped over the line of reflection. Reflecting over the x-axis: When you reflect a point across the x- axis, the x- coordinate remains the same, but the y- coordinate is transformed into its opposite.

Reflecting over the y-axis: Where do you think this picture will end up?

 Assignment  Page 25  Lets go over #7 and #8 as a class.  Page 26 # 10,11, and12 on your own!

 Question #10

 Question #11 The coordinates of A'B'C'D'E'F'G'H' are: ◦ A’(+2,+2)  B’(0,+2)  C’(0,-5)  D’(+2, – 5),  E'(+2, – 4),  F'(+3, – 4),  G'(+3, – 2),  H'(+2, – 2).

 Question #12

 Rotation: ◦ A turn about a fixed point called “the center of rotation” ◦ The rotation can be clockwise or counterclockwise.

 Assignment  Page 27  Lets go over #13 and #14 as a class.  Page # 15, 16,17, and18 on your own!

 Pg 27. #13 a) The coordinates for ∆HAT are H( – 3, – 2), A( – 1, – 3), and T( – 3, – 6). The coordinates for ∆HAT are H( – 3, – 2), A( – 1, – 3), and T( – 3, – 6). b) The rotation is 180  counterclockwise.

 Pg 27 #15. a) The coordinates for the centre of rotation are (–4, –4). b) Rotating the figure 90° clockwise will produce the same image as rotating it 270° in the opposite direction, or counterclockwise.

 #16 a) The coordinates for the centre of rotation are (+2, – 1). b) The direction and angle of the rotation could be 180° clockwise or 180° counterclockwise.

 #17 a) The figure represents the parallelogram rotated about C, 270° clockwise. b) The coordinates for Q'R'S'T' are Q'( – 1, – 1), R'( – 1, +2), S'(+1, +1), and T'(+1, – 2).

 # 18 b) The rotation image is identical to the original image.

by D. Fisher

Zebras have slightly different stripping, Ears not similar, leg bent different.

1.

2.

Reflection, Rotation, or Translation 3.

Reflection, Rotation, or Translation 3.

4.

Reflection, Rotation, or Translation 5.

Reflection, Rotation, or Translation 5.

Reflection, Rotation, or Translation 6.

Reflection, Rotation, or Translation 6

7.

Reflection, Rotation, or Translation 11. PROBABLY DOESN’T FIT ANY CATEGORY

Reflection, Rotation, or Translation 12.

Reflection, Rotation, or Translation 13. Why possibly both? Either reflected or rotated 180°

Reflection, Rotation, or Translation 14.

Reflection, Rotation, or Translation 15. REFLECTION IN SEVERAL DIRECTIONS

Reflection, Rotation, or Translation 16.

Reflection, Rotation, or Translation 17.

Reflection, Rotation, or Translation 18.

Reflection, Rotation, or Translation 19. Reflection in multiple mirrors.

Reflection, Rotation, or Translation 20.

Reflection, Rotation, or Translation 21.

Reflection, Rotation, or Translation 22.

 Assignment  Page # 1-10, 12, 15, 16, 18 and 21 on your own!

The Ultimate PowerPoint Game

Each team will hide their 4 battleships in their HIDDEN Mathematical Ocean by writing the correct number of points for each battleship with its corresponding letter All ships must be either horizontal or vertical Ships may not overlap Draw a rectangle around the correct number of points for each battleship

This is the INSIDE board. Keep this board HIDDEN from the other team!

Teams will take turns being the ATTACKERS and the DEFENDERS The ATTACKERS will select a place to attack by giving an ordered pair of numbers to the DEFENDERS The ATTACKERS will then write the ordered pair in the box to the side and circle that point on their VISIBLE Mathematical Ocean The DEFENDERS will find the coordinate on their HIDDEN Mathematical Ocean and circle it The DEFENDERS will say if the attack was a HIT ( ATTACKERS fill-in circle) or a MISS ( ATTACKERS leave circle empty) Teams will then switch roles

If the coordinate is not written in the box on the side, the attack is automatically a MISS If the coordinate is not in the Mathematical Ocean, the attack is automatically a MISS If the ATTACKERS sink one of your battleships, you must tell tell them. Otherwise you will LOSE one turn. The ATTACKERS will connect the points once the entire ship is SUNK. To WIN the game you must sink all of the the other team’s battleships before they sink all of yours

Use this board to ATTACK. Keep this board VISIBLE ! This is the OUTSIDE board.

Aircraft Carrier (5 A points) Cruiser (4 C points) Destroyer (3 D points) Submarine (2 S points) on the HIDDEN Mathematical Ocean

Use this board to HIDE your battleships. Keep this board HIDDEN from the other team! This is the INSIDE board. Battleships 1 Aircraft Carrier (AAAAA) 1 Cruiser (CCCC) 1 Destroyer (DDD) 1 Submarine (SS) Home Page

Use this board to ATTACK. Keep this board VISIBLE ! This is the OUTSIDE board.