Flashcards
Invariation
Cards in this deck (17)
- 1In terms of x and y, what represents a transformed set of points?[x'][y'] = T[x][y]
(T=transformation matrix) - 2What is an invariant point?A point which remains unchanged by a transformation
- 3What is a line of invariant points?A line where every point on it remains unchanged
- 4What is an invariant line?A line mapped onto itself. However, individual points along the line aren't necessarily mapped onto themselves.
(Mapped onto themselves = unchanged) - 5A line of invariant points is a type of an .....Invariant line
- 6What are the: single invariant points, line of invariant points and/or invariant lines of : 30 degree CW from (0,0)Single invariant points: (0,0)
Lines of invariant points: None
Invariant lines: None - 7What are the: single invariant points, line of invariant points and/or invariant lines of : X-axis reflectionSingle invariant points: None
Lines of invariant points: X-axis
Invariant lines: None - 8What are the: single invariant points, line of invariant points and/or invariant lines of : y=-x reflectionSingle invariant points: None
Lines of invariant points: y=-x
Invariant lines: y=x+c - 9What are the: single invariant points, line of invariant points and/or invariant lines of : Stretch factor 2 in x-directionSingle invariant points: None
Lines of invariant points: Y-axis
Invariant lines: y=c - 10What are the: single invariant points, line of invariant points and/or invariant lines of : Enlargement sf 3 from (0,0)Single invariant points: (0,0)
Lines of invariant points: None
Invariant lines: y=mx - 11What are the: single invariant points, line of invariant points and/or invariant lines of : Reflection in y=2xSingle invariant points: None
Lines of invariant points: y=2x
Invariant lines: y=-1/2x+c - 12What are the: single invariant points, line of invariant points and/or invariant lines of : Stretch factor 1/2 in y-directionSingle invariant points: None
Lines of invariant points: X-axis
Invariant lines: x=c - 13What lines does the invariant line y=mx represent?X-axis , Y-axis , y=x , y=-x
- 14What does "c" represent (e.g. x=c)?1,2,3 etc
(x=1, x=2, x=3 etc) - 15If M[x][y] = [x'][y'] and M=[-1 5][4 -9], describe a method to find the line of invariant points1. Multiply M by [x][y] and remove brackets to get -x+5y and 4x-9y. We can set these = to x and y like it says in the question.
2. Rearrange for 0 in both equations.
3. One equation will be -2x+5y=0, so rearrange for 5y=2x, and again to y=2/5x. This is the line of invariant points. - 16To find an invariant line, we must....Find the image of y=mx+c (in terms of y' and x') and sub this into y'=mx'+c
- 17If a line has the equation y=mx+c, a point (x,y) on the line can be written as.....(x,mx+c)
([x'][y'] = T[x][mx+c])