Back to 课程

Further Maths: Core Pure -Edexcel-A Level

0% Complete
0/0 Steps
  1. complex-numbers-and-argand-diagrams
    6 主题
  2. exponential-form-and-de-moivres-theorem
    4 主题
  3. properties-of-matrices
    3 主题
  4. transformations-using-matrices
    3 主题
  5. roots-of-polynomials
    2 主题
  6. series
    2 主题
  7. maclaurin-series
    1 主题
  8. hyperbolic-functions
    4 主题
  9. volumes-of-revolution
    2 主题
  10. methods-in-calculus
    5 主题
  11. vector-lines
    4 主题
  12. vector-planes
    4 主题
  13. polar-coordinates
    2 主题
  14. first-order-differential-equations
    3 主题
  15. second-order-differential-equations
    2 主题
  16. simple-harmonic-motion
    2 主题
  17. proof-by-induction
    2 主题
课 Progress
0% Complete

Invariant points

What is an invariant point?

  • When applying transformations to a shape or collection of points, there may be some points that stay in their original position; these are known as invariant points

How can I find invariant points?

  • If the point given by position vector text bold x end text text ; end text space open parentheses table row x row y end table close parentheses, is invariant under transformation text bold T end text semicolon space open parentheses table row a b row c d end table close parentheses then we can say that text bold Tx end text text = end text text bold x end text

    • <img alt=”open parentheses table row a b row c d end table close parentheses open parentheses table row x row y end table close parentheses equals open parentheses table row x row y end table close parentheses” data-mathml='<math ><semantics><mrow><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr></mtable></mfenced><mfenced><mtable><mtr><mtd><mi>x</mi></mtd></mtr><mtr><mtd><mi>y</mi></mtd></mtr></mtable></mfenced><mo>=</mo><mfenced><mtable><mtr><mtd><mi>x</mi></mtd></mtr><mtr><mtd><mi>y</mi></mtd></mtr></mtable></mfenced></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″}</annotation></semantics></math>’ height=”54″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2254%22%20width%3D%22131%22%20wrs%3Abaseline%3D%2233%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfenced%3E%3Cmtable%3E%3Cmtr%3E%3Cmtd%3E%3Cmi%3Ea%3C%2Fmi%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmi%3Eb%3C%2Fmi%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmi%3Ec%3C%2Fmi%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmi%3Ed%3C%2Fmi%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmfenced%3E%3Cmfenced%3E%3Cmtable%3E%3Cmtr%3E%3Cmtd%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmtd%3E%3C%

Responses

您的邮箱地址不会被公开。 必填项已用 * 标注