Mathematics Dictionary

Mathematics Dictionary
Dr. K. G. Shih

Transformation Matrix

Subjects

Example : Sqr(x) is square root of x

Q01 | - Transformation : Demo

Q02 | - Transformation : Input data

Q03 | - Transformation : Circle

Q04 | - Transformation : parabola

Q05 | - Transformation : Ellipse

Q06 | - Application : Transformation of circle

Q07 | -

Q08 | -

Q09 | -

Q10 | -

Answers

Diagrams
- Analytic geometry Transormation and translation
- Examples : Program 12 03
  - Click section 12 in upper box
  - Click progam 01 in lower box
  - Click re-plot or press Enter key to see next one
Examples : Program 12 01
- It contains 11 transformation matrix
- Write down the matrix
- Describe the trnsformation
- First matrix is transformation to make graph smmetrical to y = x
  - | +0 +1 |
  - | +1 +0 |
- To see 2nd trnasformation, click Re-plot
- To see 3rd trnasformation, click Re-plot again
Home work
- 1. Find the transformation matrix to make graph symmetrical to x-axis
- 2. Find the transformation matrix to make graph symmetrical to y-axis
- 3. Find the transformation matrix to make graph symmetrical to y = -x
- 4. Find the transformation maxtix to change the shape of the graph

Diagrams
- Analytic geometry Transormation and translation
- Method to use
  - Click section 12 in upper box
  - Click progam 02 in lower box
Prepare data for program 12 02
- Mmatrix data : a11, a21, a12, a22
- Example of matrix data
  - | +0 +1 | This is 1st row : a11 = 0 and a21 = 1
  - | +1 +0 | This is 2nd row : a11 = 1 and a21 = 0
Home work
- 1. Find the transformation matrix to make graph symmetrical to x-axis
- 2. Find the transformation matrix to make graph symmetrical to y-axis
- 3. Find the transformation matrix to make graph symmetrical to y = -x
- 4. Find the transformation maxtix to change the shape of the graph

Diagram
- Analytic geometry Transormation and translation
- Examples : Use program 12 05
  - Click section 12 in upper box
  - Click progam 04 in lower box
  - Click re-plot or press Enter key to see next one
Equation of parabola
- Polar form : R = D/(1 - sin(A)) where D is the distance of focus to directrix
- Rectangular : y - k = (x - h)^2/(2*D)
Diagram of the parabola is in polar form R = D/(1 - sin(A))
- The focus is at (xf, yf). What are the values of xf and yf ?
- What are the coordiante of the vertex (xv,yv) ?
- The distance between vertex and focus is D/2. Write down equation of directrix
- Write down the equation of pricipal of axis
- What is the value of D ?
Write down the equation of parabola in polar form after the transformation
- The transformation matrix
- The equation of parabola in polar form if it is congruent to origin graph
Reference
- Analytic geometry Parabola

Diagram
- Analytic geometry Transormation and translation
- Examples : Use program 12 05
  - Click section 12 in upper box
  - Click progam 05 in lower box
  - Click re-plot or press Enter key to see next one
Equation of ellipse in polar form
- Polar form : R = (D*e)/(1 - e*sin(A)) or R = (D*e)/(1 - e*cos(A))
- D is the distance of focus to directrix
- e is the f/a and f is the focal length and e is less than 1
Rectangular : ((x-h)/a)^2 + ((y-k)/b)^2 = 1
- (h,k) is the center
- The semi-axese are a abd b
Diagram of the ellipe is in polar form R = (D*e)/(1 - e*sin(A))
- The focus is at (xf, yf). What are the values of xf and yf ?
- What are the coordiante of the vertices (xu,yu) and (xv,yv) ?
- The distance between vertex and focus is a - f.
- How to find D ?
- Write down the equation of pricipal of axis
- What is the value of D ?
Write down the equation of ellipse in polar form after the transformation
- The transformation matrix
- The equation of parabola in polar form if it is congruent to origin graph
Reference
- Analytic geometry Ellipse

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