What is the smallest possible distance between the point (0, 5) and an

Question

What is the smallest possible distance between the point (0, 5) and any point on the line  y = -x + 3 ?

A.  0

B.  \frac{1}{\sqrt{2}}

C.  1

D.  \sqrt{2}

E.  2

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Kinshook · Accepted Answer

Asked: What is the smallest possible distance between the point (0, 5) and any point on the line  y = -x + 3 ?

Shortest distance from a point (m, n) from a line {ax + by + c = 0 } =  |am+bn+c|/\sqrt{a^2 + b^2} 
Equation of the line : x + y - 3 = 0 
Shortest distance of the line from point (0,5) =  |0+5-3|/\sqrt{2} = 2/\sqrt{2} = \sqrt{2}

IMO D

GMATinsight · Answer

Answer: Option D

Step-by-Step Video solution by  GMATinsight

https://www.youtube.com/watch?v=T9pvqQb54Ig

false9 · Answer

One way to get shortest possible distance between a point and a line is to draw a line that passes through the given point (0,5) and is perpendicular to the give line (x+y=3), and then calculating the distance between the intersection point of these two line and the given point (0,5). 
Given line here : x+y=3

Line perpendicular to given line: x-y = Constant (K). K can be calculated as this line passes through (0,5). K= -5.

Intersection point of these two lines will be (-1,4).

Distance between (0,5) and (-1,4) = √2

saynchalk · Answer

too many steps involved, what's the likelihood of this being asked in GMAT focus?  Bunuel   chetan2u

Krunaal · Answer

Quickest way is to remember the formula to find shortest distance between ax + by + c = 0 and ( x_1 , y_1 ) =  |ax_1+by_1+c|  /  \sqrt{a^2+b^2}

What is the smallest possible distance between the point (0, 5) and an

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