Maths-
General
Easy

Question

If the axes are rotated through an angle of 45° and the point p has new co-ordinates left parenthesis 2 square root of 2 comma square root of 2 right parenthesis then original coordinates of p are

  1. (1,3)
  2. (-1,3)
  3. (3,1)
  4. (3,3)

hintHint:

Find the coordinates of a point from the rotation matrix of given angle and the new coordinates.

The correct answer is: (1,3)


    Given That:
    If the axes are rotated through an angle of 45° and the point p has new co-ordinates left parenthesis 2 square root of 2 comma square root of 2 right parenthesis then original coordinates of p are
    >>> let theta be the angle of rotation then the coordinates becomes:
    x equals X cos theta plus Y sin theta
y equals negative X sin theta plus Y cos theta
    >>> Then, the points becomes:
    x equals 2 square root of 2 cos left parenthesis 45 right parenthesis plus square root of 2 sin left parenthesis 45 right parenthesis
x equals space 3
    y equals negative 2 square root of 2 sin left parenthesis 45 right parenthesis space plus space square root of 2 cos left parenthesis 45 right parenthesis
y equals 1
    >>> Therefore, the original point is (3,1).

    >>> Therefore, the original point is (3,1).

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