The line `P Q` whose equation is `x-y=2` cuts the x-axis at `P` ,and `Q` is (4,2). The line `P Q` is rotated about `P` through `45^@` in the anticlockwise direction. The equation of the line `P Q` in the new position is (A) `y=-sqrt(2)` (B) `y=2` (C) `x=2` (D) `x=-2`

Options

A. `y=-sqrt(2)`
B. y=2
C. x=2
D. x=-2

Explanation

To solve the problem step by step, we will follow the process of finding the coordinates of point P, determining the slope of line PQ, and then rotating the line by 45 degrees anticlockwise about point P.

### Step 1: Find the coordinates of point P
The equation of the line is given as \( x - y = 2 \). To find the x-intercept (point P), we set \( y = 0 \):

\[ x - 0 = 2 \implies x = 2 \]
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