Geogebra 6
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This document provides instructions for using a graphing calculator to explore linear inequalities and integer addition visually. It guides the user to create sliders and points on a number line to represent linear expressions and the addition of integers. Adjusting the sliders allows observation of how changing the variables affects the linear inequality and integer sum. The final construction enhances understanding through an interactive visualization of these mathematical concepts.
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On the tomcat drive in folder cosc210 you will find file named Paint.docx
On the tomcat drive in folder cosc210 you will find file named PainterStartup.zip. This file contains the source code for the start of a Painter program. In its current state, Painter can create boxes and text objects at given locations. Both boxes and text objects can be repositioned and resized using a mouse. The task is to add to the program the implementation for an oval, line, image, and group objects.
Instructions:
Add an oval object. An oval is very similar in implementation as the box, except it renders an oval instead of a rectangle. The oval can be repositioned by dragging the object to a new location. The oval can be resized by first clicking over the oval to display grab handles and then dragging a grab handle to a new position. The grab handles are to be rendered at the same positions as the box. Likewise, clicking anywhere in the smallest rectangle that encloses the oval performs selection.
Add a Line object. A Line is to be created by selecting a Line tool and then click and drag over the canvas. The line is rendered from the point of the initial click to the mouse pointer. On releasing the mouse the construction of the line object is completed. A partial implementation of a PtrDrawLine object is provided. You will need to fix the rendering, click over, and test for inside a rectangle.
A Line is selected by clicking anywhere over the line. Right now if you click anywhere in the rectangular region hold the line, then the line is selected. The implementation is in the isOver method. This needs to be fixed to only select when the click is on the line.
Given below is a partial solution to determine if a mouse click position (the x and y parameters to the isOver method) is over a line:
double ratio = (double) getDeltaY( ) / (double) getDeltaX( );
if (Math.abs(((x - getX( )) * ratio) - (y - getY( ))) <= 1) {
return true;
}
You need to modify this code when the y to x ratio is less than -1 or greater than 1. (hint: Inverse the roles of x and y)
The isInside method provides the implementation for determining if the line is inside a rectangular area as specified by the parameters. This code does not work right if the ending point of the line is to the left or above the starting point. Fix this to work in all cases.
Add an Image object. An Image object is created by selecting an Image tool and then clicking anywhere on the canvas. On clicking the canvas, a File Selection Dialog should be displayed. The dialog prompts for selection of .gif and .jpg files. On selecting a .gif or .jpg file and clicking “Open”, an Image object that renders the image of the selected file is created at the click position. Image selection and drag behaviors are the same as a Box object. The image object additionally renders lines at the edges of the image (as done in Box).
The code for displaying a File Selection Dialog is:
JFileChooser fileChooser = new JFileChooser();
f.
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S7 investigating vectors student worksheet (colour)
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Chapter 13
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1 Instructions Solve the following problems, showing all.docx
1
Instructions: Solve the following problems, showing all of your work for full credit
.
Problem 1: (10 Points)
(A)
Given
73
1
))(()(
+
==
x
xgfxh
Find
i) )(xf ii) )(xg
(B)
For the function given below, construct and simplify the difference of
Quotient
a) 42)( 2 −= xxf
MA112/109
2
Problem 2: (20 Points)
A)
. Consider the parabola of equation 56)( 2 +−= xxxf
a) Find the vertex by completing the square
b) Find the axis of symmetry
c) Find
i) x- intercept ii) y-intercepts
d) Sketch the graph of ( )f x
MA112/109 EXAM II
3
Problem 3: (15 Points)
Given
≥+
<+−
=
1,1
1,13
)( 2 xifx
xifx
xf
a) Find
i) )1(−f = ii) )0(f =
iii) )1(f iv) )2(f =
b) Sketch an accurate graph of f
MA112/109
4
Problem4: (15 Points)
(A)
Write the equation of the function that has the shape of 3xy = , but shifted left 3
units and up 4 units
(B)
Find the exact solution:
3
9
3
2
−
=
− xx
x
-
(C) Solve and write the interval notation for the solution set and graph solution
set
Solve: 215 ≥+ x
5
Problem 6;
f (x) = x+2 and g(x) = 1−x , find each of the following. (5 points)
a) Domain of f(x):
b) Domain of g(x):
c) Domain of (f + g) (x):
d) Find (f/g)(x) =
e) Domain of (f/g)(x) =
Problem 7:
(5, Points)
Given functions: 13)( += xxf , 62)( 2 −−= xxxg and 2)( xxh =
a) Find ( )( )xgfxk =)(
6
b) Find ( )( )2)( hfxl =
Problem 8:
Graph the following function: ...
Basic Graphics in Java
This document provides an overview of basic graphics and animation capabilities in Java. It discusses how to draw various shapes like lines, rectangles, ovals, arcs and polygons using the Graphics class. Key methods for drawing shapes are described, including drawLine(), drawRect(), drawOval(), drawArc(), and drawPolygon(). Examples are given to demonstrate how to use these methods to draw simple shapes and composite figures like a human face. The document also explains Java's coordinate system and how shapes are drawn within the canvas area.
Windows and viewport
This document discusses coordinate systems and mapping between world coordinates and screen coordinates in OpenGL. It explains that:
1) Objects are defined using world coordinates, while screens use pixel coordinates, so OpenGL maps between these spaces.
2) The world window defines the region of the world coordinates that will be drawn, and the viewport defines the screen region it will be drawn to.
3) OpenGL uses a linear transformation to map world to screen coordinates, defined by scaling and translation constants A, B, C, and D that are calculated based on the world window and viewport sizes.
Commly used shapes and designs for powerpoint
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Computer Graphics in Java and Scala - Part 1b
First see the Scala program from Part 1 translated into Java.
Then see the Scala program modified to produce a more intricate drawing.
Java Code: https://github.com/philipschwarz/computer-graphics-50-triangles-java
Scala Code: https://github.com/philipschwarz/computer-graphics-chessboard-with-a-great-many-squares-scala
Esurveying Contour software
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ENGR 102B Microsoft Excel Proficiency LevelsPlease have your in.docx
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On the tomcat drive in folder cosc210 you will find file named Paint.docx
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S7 investigating vectors student worksheet (colour)
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Geogebra 6
- 3. Linear Inequalities Task Graph a linear inequality ax + b ≤ c that can be explored using sliders.
- 4. Enter ax + b ≤ c into the Input Bar and press Enter. Hint: You can use the Virtual Keyboard to enter the ≤ symbol. GeoGebra will automatically create sliders for the parameters a, b, and c
- 5. Use the Move tool to adjust the slider values so that a = 1, b = 1, and c = 3.
- 6. Change the increment of the sliders to 1. Hints: Select number a and open the Style Bar of the Graphics View. Style Bar Select number a
- 7. . Slider tab Increment Open the Settings of number a and select tab Slider. Set the Increment to 1 and repeat for numbers b and c Settings
- 8. Drag the background of the Graphics View to move the origin to the center
- 9. Zoom Out to make a bigger part of the coordinate system visible on screen Zoom out
- 10. Set the distance between the marks on the axes to 1. Hints: Make sure that no object is selected before you open the Style Bar of the Graphics View. Open the Settings of the axes. Select tab xAxis and set the Distance to 1. Repeat on tab yAxis. Make sure no object is selected Change Distance
- 11. Finally, you can select all objects and animate. What do you observe?
- 12. Visualizing Integer Addition Task Create a dynamic figure that visualizes the addition of integers on the number line.
- 13. Open the Settings of the Graphics View using the Style Bar
- 14. On tab xAxis set the distance of tick marks to 1 by checking the box Distance and entering 1 into the text field. Change Distance
- 15. On tab Basic set the minimum of the xAxis to -11 and the maximum to 11 Set here
- 16. On tab yAxis uncheck Show yAxis and close the Settings. Uncheck Show yAxis
- 17. Create two sliders a and b, both with Interval -5 to 5 and Increment 1 Sliders a and b
- 18. Show the value of the sliders instead of their names using the Style Bar Change here
- 19. Create points A = (0 , 1) and B = A + (a , 0). Hint: The distance of point B to point A is determined by slider a Points A and B
- 20. Create a vector u = Vector(A, B) which has the length a Vector u
- 21. Create points C = B + (0, 1) and D = C + (b, 0) Points C and D
- 22. Create vector v = Vector(C, D) which has the length b Vector v
- 23. Create point R = (x(D), 0). Hint: The input x(D) gives you the x-coordinate of point D. Thus, point R shows the result of the addition on the number line Point R
- 24. Create point Z = (0, 0) Point Z
- 25. Create three segments c = Segment(Z, A), d= Segment(B, C), and e = Segment(D, R) Segments
- 26. Use the Style Bar to enhance your construction (e.g. match the color of sliders and vectors, change line style, fix sliders, hide labels and points).