Exams › SSC CGL (Prelims) › General

What is the minimum distance from the origin $(0,0)$ to a point on the line segment connecting the points $A(6,0)$ and $B(0,8)$?

1. 3.6
2. 4.2
3. 4.8
4. 5.4

Correct answer: 4.8

Solution

The line through $(6,0)$ and $(0,8)$ is $\frac{x}{6}+\frac{y}{8}=1$, or $4x+3y=24$. The distance from the origin to this line is $\frac{|24|}{\sqrt{4^2+3^2}}=\frac{24}{5}=4.8$. Since the perpendicular foot lies on the segment, this is the minimum distance.

Related SSC CGL (Prelims) General questions

• What is the equation of a line passing through \((0,4)\) with slope \(-2\)?
• What is the slope of the line perpendicular to $y = 5x - 8$?
• Which line has slope \(-2\) and passes through \((3,5)\)?
• A line \(L\) is the perpendicular bisector of the line segment joining points \(P(4,6)\) and \(Q(10,2)\). What is the y-intercept of line \(L\)?
• Find the slope of the line $4x - 5y = 10$.
• Find the equation of the perpendicular bisector of the line segment joining the points $(1,5)$ and $(5,9)$.

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