Perpendicular Distance of a Point from a Line

Q. The sum of the intercept cut off by the axes on lines $x+y=a,x+y=ar,x+y=a{r}^2,....$ where $a\ne 0$ and $r=\frac{1}{2}$

1. $2a$
2. $a\sqrt{2}$
3. $2\sqrt{2}a$
4. $4a$

Q. The length of the perpendicular line - segment from origin to line $x-\sqrt{3}y+4=0$ is _______.

1. -1
2. 2
3. 4
4. 1

Q. The perpendicular bisector of the line segment joining $P(1,4)$ and $Q(k,3)$ has y-intercept $-4$. Then a possible value of $k$ is

1. 1
2. 2
3. -2
4. -4

Q. Find the distance of a point $(3,4)$ from the line $4x-3y=12$.