Coordinate Geometry
JC Coordinate Geometry
Table of Contents
- The Point Chapter
- What are the Coordinates of the Point
- Bee's Journey: Non-negative Coordinates Exploration gt5a
- Pairing Points to Coordinates gt5a
- The Quadrants of the Plane gt5a
- Treasure hunt gt5
- Cannon Fire at Ship's Coordinate Point gt5a
- Treasure in Four Quadrants GT5a
- graph and Table of a set of points gt5a
- Investigate Collinear Points using Slopegt5c
- Angles and Quadrants
- Explore Group of Points in a Quadrant gt5
- Drag Points to Matching Coordinate AAL
- The Distance Chapter
- Line Segment Length gt5a
- Distance between Two Points
- GT5 Coordinate Distance
- Length of Horizontal or Vertical Line Segments 水平或鉛垂線段的長度
- The Midpoint Chapter
- Midpoint Calculations Exploration
- Mid-value of Two Integers
- Midpoint of Two Coordinates
- Understand the Midpoint of a Line Segnent
- Midpoint of a line segment gt5
- Midpoint construction
- Quadrilateral Midpoints forming parallelogram
- Triangle Midsegment Explore line segment
- The Slope Chapter
- Types of slopes- multiple choice
- Types of slope - AAL
- Graph to Slope Task
- Slope to graph Task
- Slope Shooting Game
- Point-Slope Graphs GT5a
- Slope from coordinates scaffolded_AAL
- Slope from coordinates AAL
- Slope shoot baloon 2 gt5a
- Explore concept of slope gt5a
- Horizontal and vertical lines slopes
- Quiz on Slope (1) | 斜率測驗(1)
- Slope and y-intercept
- Slope Intercept
- Copy of Copy of Equation of Straight Lines 直線的方程
- Points of Intersection
- The Line Chapter
- Determine the Intercepts of a Line Stated in Standard Form
- Slope Intercept Form
- Copy of Slope Intercept Form
- Linear graph interactive
- Line Segments
- Polygon Explorer
- Classifying Polygons
- Triangle Midsegment Explore line segment
- Translations Chapter
- Translations
- Translation Triangle
- Translation components
- Monster Translation
- Translation as coordinates
- Two colour coded Translations
- Translation vector coordinates gt6
- Rigid Congruent Transformations -Including translation
- Copy of Triangle Midsegment
- The Extra Challenge Chapter
- Slope and Points: Open Middle Challege gt5
What are the Coordinates of the Point
[size=150]The distance of a point from the y-axis, scaled with the x-axis, is called abscissa or x coordinate of the point. The distance of a point from x-axis scaled with the y-axis is called ordinate.[/size]
Line Segment Length gt5a
Distance Formula
Midpoint Calculations Exploration
Midpoint Coordinate
Types of slopes- multiple choice
" The "slope" of a line in a coordinate plane describes how steep the line is, and it is determined by the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.
Determine the Intercepts of a Line Stated in Standard Form
Determine the Intercepts of a Line Stated in Standard Form
Note: [br]1.To find x-intercept, put y=0.Hence x-intercept =[math]\frac{c}{a}[/math][br]2.To find y-intercept, put x=0.Hence y-intercept =[math]\frac{c}{b}[/math]
Copy of Slope Intercept Form
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Use the two points to graph the line.
Slope Intercept Form
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1. Use the worksheet provided by Mr. Cox.[br]2. Once you are an [b]expert[/b] at graphing lines in slope intercept form, go to [url]http://www.geogebratube.org/student/m821[/url] and work on Standard Form equations.
Polygon Explorer
Translations
When teaching translations and transformations to students, it's essential to embed certain key vocabulary and foundational ideas to ensure they grasp these concepts thoroughly. Below is a guide to the critical terms and concepts for each topic.[br][br]### Translations[br][br]1. **Translation**:[br] - Definition: A transformation that slides every point of a shape the same distance in the same direction.[br] - Key Vocabulary: Slide, Direction, Distance, Transform, Shift.[br][br]2. **Vector**:[br] - Definition: A quantity with both magnitude and direction. It describes the direction and distance of the translation.[br] - Key Vocabulary: Vector, Magnitude, Direction.[br][br]3. **Coordinate Notation**:[br] - Definition: A method to describe the translation, showing how much a point moves in the x-direction and y-direction.[br] - Key Vocabulary: Coordinate plane, (x, y), Movement along x-axis, Movement along y-axis.[br][br]4. **Mapping Rule**:[br] - Definition: A rule that explains how each point in the shape is moved to its new location. For example, (x, y) → (x + a, y + b).[br] - Key Vocabulary: Rule, Map, Move.[br][br]### Transformations[br][br]1. **Transformation**:[br] - Definition: A general term for any change in position, shape, or size of a figure.[br] - Key Vocabulary: Transform, Change, Position, Shape, Size.[br][br]2. **Rigid Transformation** (Isometry):[br] - Definition: Transformations that preserve distance and angle, so the shape does not change size or shape.[br] - Key Vocabulary: Rigid, Isometry, Preserve, Distance, Angle.[br][br]3. **Non-Rigid Transformation** (Dilation):[br] - Definition: Transformations that change the size of a figure but keep its shape.[br] - Key Vocabulary: Non-rigid, Dilation, Scale, Enlarge, Reduce.[br][br]4. **Types of Transformations**:[br] - Translations (as above), Rotations, Reflections, and Scaling.[br] - Key Vocabulary: Rotate (Turn), Reflect (Flip), Scale (Resize), Center of rotation, Angle of rotation, Line of reflection, Scale factor.[br][br]5. **Congruence and Similarity**:[br] - Definition: Congruence relates to shapes that are identical in shape and size after a transformation. Similarity refers to shapes that are proportional but not necessarily the same size.[br] - Key Vocabulary: Congruent, Similar, Proportional, Identical.[br][br]6. **Composition of Transformations**:[br] - Definition: Performing more than one transformation on a figure. For example, a translation followed by a rotation.[br] - Key Vocabulary: Composition, Sequence, Successive, Combine.[br][br]### Foundational Ideas[br][br]- **Invariance**: Emphasize which properties (like angles, distances, parallelism) remain unchanged under various transformations.[br]- **Coordinate System Understanding**: Reinforce the use of the Cartesian coordinate system to describe positions and movements.[br]- **Visual and Spatial Reasoning**: Encourage students to visualize transformations and understand the spatial relationships between figures before and after transformations.[br]- **Problem-Solving and Application**: Engage students in applying these concepts to solve problems, including real-life scenarios where possible.[br][br]Integrating these vocabulary terms and foundational ideas into your teaching will help students develop a robust understanding of translations and transformations, setting a solid foundation for more advanced mathematical concepts.
Slope and Points: Open Middle Challege gt5
Can you create a setup where all four slope statements (on the left) are true?
In each app below, move points [b]A, B, C, [/b]and [b]D [/b]around (on the right side). Use the given digits 1-9 no more than 1 x each to fill in the boxes [b]so that all four slope statements become true[/b]. [br][br][list][*]When a slope statement becomes [b]true[/b], a [b]"true" [/b]sign will appear! [/*][*]Use the [b]+ or -[/b] buttons to change the sign of the given slope at any time. [/*][*]Use the custom [b]SLOPE TRIANGLE TOOL [/b]to show the slope triangle for the line between any two points. [/*][/list]