Question

A particle starting from the point $(1,2)$ moves in a straight line in $XY$-plane. Its coordinates at a later time are $(2,3)$. The path of the particle makes with $x$-axis an angle of

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. Data sufficient

Answer 1

The correct option is B ${45}^{\circ }$

Since the particles move along a straight line. This means that the given coordinates lie on the line on which the particle moves.

So, we have to find the angle which this line makes with the X axis.

I.e the slope of this line which is given by $tan\theta$

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

$\therefore \theta =\frac{\pi }{4}={45}^{\circ }$