Question

The distance of the point (1, 2) from the straight line with slope 5 and passing through the point of intersection of lines x + 2y = 5 and x – 3y = 7 is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

The two lines x + 2y = 5 and x – 3y = 7 intersect at the point P$(\frac{29}{5},-\frac{2}{5})$

Equation of the line through the point P $(\frac{29}{5},-\frac{2}{5})$ having slope 5 is

$y+\frac{2}{5}=5(x-\frac{29}{5})or5y+2=5(5x-29)$

or 25x – 5y – 147 = 0 …… (1)

Now, length of the perpendicular from the point (1, 2) to the line (1) is

$P=\frac{|25\left(1\right)-5\left(2\right)-147|}{\sqrt{(25{)}^2+5^2}}=\frac{132}{\sqrt{650}}$