Question

The line AB whose equation is x-y=2 cuts the x-axis at A and B is (4,2). the line segment AB is rotated about 'A' through an angle ${45}^{\circ }$ in the anticlockwise sense . then the equation AB in new position is

• A. $x=2$
• B. $x-1=0$
• C. $x-\sqrt{2}y-2=0$
• D. $y-2=0$

Answer 1

The correct option is A $x=2$

We have,

Given equation of line AB is $x-y=2$ …… (1)

Cuts the X-axis at point A.

So, y=0 at point A.

$x-0=2$

$x=2$

Point A is $(2,0)$.

So,

$x-y=2$

$\Rightarrow y=x-2$

Slope of line $m_1=1$

We know that,

$m_1=\tan \theta =\tan {45}^o$

$m_1=1$

So, after rotating,

It will be making ${90}^o$

Angle with positive X-axis.

So, slope $=\tan {90}^o=\infty$

Now, equation of AB is new position

$y-0=\tan {90}^o(x-2)$

$\Rightarrow y=\frac{1}{0}(x-2)$

$\Rightarrow x-2=0$

$\Rightarrow x=2$

Hence, this is the answer.