The equation of line AB which makes an equal intercepts on positive x and y axes are
x
a
+
y
a
=1 ie, x+y=a . . . (i) Distance of Eq. (i) from origin =1 |
0+0−a
√1+1
|=1,|
−a
√2
|=1 ⇒a=√2 From Eq. (i), x+y=√2 . . . (ii) Also given line, 2x−y=−3−√2 . . . (iii) The intersection point of line (ii) and line (iii) is (x0,y0)=(−1,√2+1) So, 2x0+y0=2(−1)+√2+1 =−2+√2+1=(√2−1) Hence, 2x0+y0=√2−1