Co-ordinate axes are rotated through an angle of 45- in the anti-Clockwise direction- Find the Co-Ordinates of 2-3 in new co-ordinate system-

The correct option is D Rotating the co ordinate axes through an angle of 45^∘ in anti clockwise direction is equivalent to rotating the point through an angl ...

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Byju's Answer

Standard XI

Mathematics

Rotation of Axes

Co-ordinate a...

Question

Co-ordinate axes are rotated through an angle of $45^{\circ}$ in the anti-Clockwise direction. Find the Co-Ordinates of (2,3) in new co-ordinate system.

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Solution

The correct option is D

Rotating the co-ordinate axes through an angle of $45^{\circ}$ in anti-clockwise direction is equivalent to rotating the point through an angle of $- 45^{\circ}$ about origin.We will use rotation from complex numbers to solve this.

Let x + iy the new complex number

x + iy = $(2 + 3 i) e^{\frac{- i π}{4}}$

= $(2 + 3 i) (\frac{1 - i}{\sqrt{2}})$

= (2 - 2i + 3i + 3) $\times \frac{1}{\sqrt{2}}$

=(5 + i) $\times \frac{1}{\sqrt{2}}$

$\Rightarrow (\frac{5}{\sqrt{2}}, \frac{1}{\sqrt{2}})$ is the co-ordinate system.

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Q. The axes of co-ordinates are rotated about z-axis through an angle of

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Co-ordinate axes are rotated through an angle of 45∘ in the anti-Clockwise direction. Find the Co-Ordinates of (2,3) in new co-ordinate system.

Co-ordinate axes are rotated through an angle of $45^{\circ}$ in the anti-Clockwise direction. Find the Co-Ordinates of (2,3) in new co-ordinate system.