MCQ
A line $y = x$ is rotated through $60^\circ $. Find the new angle made by line with $X$ axis.
- ✓$105^\circ $
- B$135^\circ$
- C$155^\circ$
- D$120^\circ$
✓
Answer
Correct option: A.
$105^\circ $
Given $y = x$ slope of line
$\text{m}=\tan\theta=\frac{\text{dy}}{\text{dx}}$
$\text{m}=\tan\theta=\frac{\text{d}(\text{x})}{\text{dx}}$
$\text{m}=\tan\theta=1$
hence $\theta=45^\circ$
Now rotate the line anti - clockwise through $60^\circ $
So angle makes by new line with positive $X$ - axis is $45^\circ + 60^\circ = 105^\circ .$
$\text{m}=\tan\theta=\frac{\text{dy}}{\text{dx}}$
$\text{m}=\tan\theta=\frac{\text{d}(\text{x})}{\text{dx}}$
$\text{m}=\tan\theta=1$
hence $\theta=45^\circ$
Now rotate the line anti - clockwise through $60^\circ $
So angle makes by new line with positive $X$ - axis is $45^\circ + 60^\circ = 105^\circ .$
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