Question

The origin is shifted to (m,2) and the axes are rotated through an angle of ${90}^{\circ }$ anti clockwise. The new co-ordinates of P(3,5) is (3,-2) . Find the value of m.

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Answer 1

After translation of origin to the point (m,2) the coordinates of P(3,5) becomes (3-m,5-2) = (3-m,3)

After rotating the axes through ${90}^{\circ }$

(3 - m + 3i) becomes (3 - m + 3i)$e^{\frac{-i\pi }{2}}$

= (3 - m + 3i) - i

= 3 - i(3 - m)

$\Rightarrow$ (3,-(3-m))

are the new coordinates.

This is given as (3,-2)

$\Rightarrow$ -2 = -(3-m)

$\therefore$ m=1