Question

Given three straight lines `2x+11 y-5=0,24 x+7y-20=0,` and `4x-3y-2=0` . Then, they form a triangle one line bisects the angle between the other two two of them are parallel
A. 12 and 4 respectively
B. 11 and 5 respectively
C. Equal to each other
D. Not equal to each other

Answer 1

Correct Answer - C
We know, the perpendicular distance (d) from point `(x_(1), y_(2))` to line `ax+by+c=0` is `(|ax_(1)+by_(1)+c|)/sqrt(a^(2)+b^(2))`.
Let us find a point on line `2x+11y-5=0`.
for `x=0, 2(0)+11y-5=0`
`implies 11y-5=0`
`implies y=5/11`.
So, `(x, y)=(0, 5/11)`
Let us find perpendicular distances of this point to the gives lines.

`:. d_(1)=d_(2)`