Question

Find the coordinates of $(2,3)$ if axes are rotated by an angle of ${45}^o$ in clockwise sense

• A. $(-\frac{2}{\sqrt{2}},\frac{5\sqrt{2}}{2})$
• B. $(5\sqrt{2},\sqrt{2})$
• C. $(5,\sqrt{2})$
• D. $(\frac{5\sqrt{2}}{2},-\frac{\sqrt{2}}{2})$

Answer 1

The correct option is A $(-\frac{2}{\sqrt{2}},\frac{5\sqrt{2}}{2})$

Given that,

co ordinate = $(2,3)$

angle $={45}^o$

clockwise, rotation ,

then, we know that

New coordinate are

$x^{\prime }=x\cos \theta -y\sin \theta ,y^{\prime }=x\cos \theta +y\sin \theta$

$x^{\prime }=2\cos {45}^o-3\sin {45}^o,y^{\prime }=2\cos {45}^o+3\sin {45}^o$

$x^{\prime }=2\times \frac{1}{\sqrt{2}}-3\times \frac{1}{\sqrt{2}},y^{\prime }=2\times \frac{1}{\sqrt{2}}+3\times \frac{1}{\sqrt{2}}$

$x^{\prime }=-\frac{1}{\sqrt{2}},y^{\prime }=\frac{5}{\sqrt{2}}$

$(x^{\prime },y^{\prime })=(-\frac{1}{\sqrt{2}},\frac{5}{\sqrt{2}})=(-\frac{2}{\sqrt{2}},\frac{5\sqrt{2}}{2})$

Hence, this is the answer.