Question

The line joining two points A(2,0),B(3,1) is rotated about A in anti-clockwise direction through an angle of 15° if B goes to C in New position then coordinates of C

Answer 1

Answer:

Step-by-step explanation:

A(2,0),B(3,1)

slope of the line AB

$=\frac{{y_2}-{y_1}}{{x_2}-{x_1}}\\\\=\frac{1-0}{3-2}$

=1

=> m = 1

That is,

$tan\theta=1\\\\\theta=45$

Therefore, the angle of inclination of line AB is 45

=>The angle of inclination of AC is 60

Now,

r=AB=AC

$r=\sqrt{ {({x_1}-{x_2})}^2+{({y_1}-{y_2})}^2}}\\\\r=\sqrt{ {(2-3)}^2+{(0-1)}^2}}\\\\r=\sqrt{2}$

The coordinates of C is

(rcos60, rsin60)

$(\sqrt{2}\frac{1}{2},\sqrt{2}\frac{\sqrt{3} }{2})\\\\(\frac{1}{\sqrt{2}},\frac{\sqrt{3}}{\sqrt{2}})$

Answer 2

Answer:

Step-by-step explanation: