| Document |
Who? |
Notes |
| Linear Transformation |
Markus Hohenwarter and
Judith Preiner
|
With GeoGebra you can also do vector arithmetic. This is used to illustrate a linear transformation by creating two vectors that form the columns of the transformation matrix. The applet will then show you the impact of this linear transformation. The construction allows you to explore virtually every possible linear transformation in a plane. Therefore you are able to investigate the characteristics of the matrix itself, as well as special transformations such as rotations by 90°, reflections in the axes, or scaling. |
| Centroid of a Quadrilateral |
Steve Blaylock |
Shows that Varignon's parallelogram collapses to the centroid |
| Parallel Varignon's |
Steve Blaylock |
Is the sides of second Varignons parallelogram parallel to the original parallelogram |
| Image of a Point |
Steve Phelps |
This file illustrates how the coordinates of the preimage (with respect to the original axis) are the same as the coordinates of the image (with respect to the transformed axis). This sketch also illustrates how the the rectangle formed by the preimage is transformed into a parallelogram whose sides lie on the column vectors. The area of this parallelogram is equal to the product of the area of the rectangle and the determinant of the matrix formed by the column vectors. This file also shows the image of the lattice points for reference. |
| Image of the Plane |
Steve Phelps |
This file illustrates the image of the plane under different 2x2 Linear Transformations. This file shows the relationship between the vectors, the matrix, and their effect on the coordinate plane. |
| Centroid Curiosity |
Steve Phelps |
created to illustrate a dynamic worksheet and to preview a concept to be introduced in the Linear Algebra course |
| Vector Operations |
Steve Phelps |
illustrates some of the vector concepts Dr. Minda discussed in the Linear Algebra class on Monday |
| Quadrilaterals of a Specific Varignon Parallelogram |
Mindy Burcham |
This illustrates the quadrilaterals that can be formed to produce a Varignon parallelogram if the parallelogram is given. It makes use of sliders to reperent one vertex of the quadrilateral. |
| Vector Equation of a Line Through Two Points |
Steve Phelps |
This mathlet illustrates the vector equation of a line using the form X=(1-t)A+tB. |
| Vector Area |
Carey Costello |
This mathlet illustrates that the area of a parallelogram can be found using two veectors. |
| Practice Problem 6 |
Kelly Shattuck |
This shows the figure associated with problem 6 from the Linear Algebra Practice Test. |
| Practice Test Problem 5 |
Catherine O'Neill |
This is practice for showing a quadrilateral is a trapezoid by using an equation. |
| Tessellate Varignon |
Kelly Harms |
Dr. Minda proposed that all quadrilaterals tessellate, and as a result Varignon quadrilaterals also cover the Euclidean plane. This applet lets you visualize and play around with this idea. |
| Diagonals of a Trapezoid |
Jillian Maher |
This applet is a demonstration of extra problem #1 from the Linear Algebra Practice Test. |
| Linear Midterm Question # 4 |
Kelly Harms |
This allows you to get a nice picture for this problem and easily see the relationship between G, G' and P. |
| Problem #5 on Practice Test |
Christy Bredestege |
This mathlet illustrates Varignon's parallelogram for quadrilaterials with a slider. See what makes it true! |
| Vector Addition for Dummies |
Christy Bredestege |
This mathlet might help you understand a little bit about basic vector addition and subtraction. |
| Unit Vectors and Sums |
Jillian Maher |
This applet explores problem #9 from the Linear Algebra midterm review - is there an angle between two unit vectors for which the sum of the vectors is still a unit vector? |
| Centroid of a Triangle |
Mindy Burcham |
This applet allows students to find the centroid of a triangle and check their answers. It also explores the centroid of the medial triangle by constructing them along with their medians. |
| Reflection of Medial Triangles |
Holly Phelps |
This worksheet explores the reflection of medial triangles. |
| Map Isometries |
Jillian Maher |
This applet is a demostration of Linear Algebra homework problem page 51 number 7. Move the line and center to change the reflection and rotation of the original triangle. Try to find which transformation makes the transformed triangle. |
| Theorem 5.7.4 |
Jere Issenmann |
Checking out how parallel lines and fix points effect area. |
| Centroid of a Parallelogram |
Teresa Munninghoff |
This allows you to see a relationship between the centroid of a parallelogram and the centroids of the two triangles that form the parallelogram. |
| #4 Linear Exam |
Teresa Munninghoff |
Given any point P inside triangle ABC and triangle A'B'C' where A',B',C' are the midpoints of the segment from the vertices to P. Check out the relationship between the centroids of the two triangles and P. |
| Composing Reflections |
Brian Bisignani |
Explore the result of composing two reflections. What transformation do you get? |
| Triangle Centers Exploration |
Brian Bisignani |
A close look at the centroid, orthocenter, circumcenter, and incenter of a triangle with two fixed points. Watch as the pathes of each is traced. |
| Transform a Triangle to a Parallelogram |
Holly Phelps |
This worksheet has you figure out our the verticies of a triangle are formed. After you figure that out you will see what type of quadrilateral if formed when you connect the verticies of the triangle with one of the image points. |
| Area of Rhombus |
Carey Costello |
This applet helps you to relate the diagonals of a rhombus to its area. |
| Proposition 2.2.1 |
Kelly Shattuck |
This applet shows you the relationship between two vectors and the angle between them. |
| Varigon's Theorem |
Jere Issenmann |
Proving Varigon's Theorem:) |
| Euler Line and Theorem |
Todd Majestic |
Just a look at the Euler line for a triangle and the relationship of the Centroid, Circumcenter, Orthocenter |
| Centroid Formula |
Veronica Robinson |
Derive a formula for calculating the centroid. |
| Test for Parallelogram |
Veronica Robinson |
This is Linear HW #2. |
| Orthodiagonal Quadrilateral |
Veronica Robinson |
This is Linear HW #5 |
| reflecting a triangle |
Mary Liz Lamb |
reflecting a triangle to locaate new vertices |
| Midsegment Connector Theorem |
Brad McDaniel |
Make a conjecture about the given picture. |
| Varignon Parallelogram |
Brad McDaniel |
Make a conjecture about the given picture. |
| Vector Addition |
Linda Johnson |
A look at how vector addition works. |
| Solutions to x^8-1=0 |
Linda Johnson |
From the notes on August 6 -- the unit circle and roots to the x^8-1=0 problem . |
| Centroids of Varignon Parallelograms |
Todd Majestic |
Notice what happens to the centroids Varignon Parallelograms |
| Minimum Perimeter of Triangle |
lbollman |
This mathlet illustrates Linear Algebra homework problem 3.4 #3. |
| This is not a linear transformation! |
lbollman |
This mathlet demonstrates that R=mU + B is not a linear transformation. |
| Medial Triangles Converge to the Centroid |
Jackie Southard |
This shows how the the repeated construction of medial triangles converges to the centroid of the original triangle. |
| Three Points Determine an Isometry |
Jackie Southard |
This shows how when given three points the isometry must be known. |
| Varignon Parallelogram |
Michael Smith |
Applet for solution to Linear Algebra Homework problem on Varignon Parallelogram |
| LA Practice Test #7 |
Michael Smith |
Applet for solution to Linear Algebra Practice Test Question #7 |
|
Quadrilateral's Interior Triangle Centroids
Varignon Vectors
|
Darron Steele |
About the first: a quadrilateral has four interior triangles. I plotted the centroids and studied them.
About the second: I drew the Varignon parallelogram of a quadrilateral using vectors.
|
| Missing point of Varignon Quad |
Melissa Keller |
Find the missing point to create a Varignon Parallelogram |
| Centroid Relationship |
Meliss Keller |
Applet that shows picture for Exam I question 4 |
Comments (6)
Steve Phelps said
at 12:27 pm on Jul 14, 2008
Kelly! your Tessellate Varignon is cool as can be!
Steve Phelps said
at 12:29 pm on Jul 14, 2008
Kelly Shattuck! Practice problem 6...I like the size of the applet window (and the sketch, too).
Steve Phelps said
at 12:30 pm on Jul 14, 2008
Catherine O! nice sketch!
Steve Phelps said
at 12:30 pm on Jul 14, 2008
Jillian! Good vector application!
Steve Phelps said
at 12:31 pm on Jul 14, 2008
Mindy! Cool picture!
Steve Phelps said
at 12:32 pm on Jul 14, 2008
Carey! Nice sketch! Remind me to show you how to put all your calculations in one big text box!
You don't have permission to comment on this page.