First slide

Equation of line in Straight lines

Question

On the portion of the straight line x + y = 2 which is intercepted between the axes, a square is constructed away from the origin, with this portion as one of its side. If p denotes the perpendicular distance of a side of this square from the origin, then the maximum value of p is

Moderate

A

$\sqrt{2}$
B

$2 \sqrt{2}$
C

$3 \sqrt{2}$
D

$4 \sqrt{2}$

Solution

p = ON = OM + MN = $⊥$ distance from
O to the line AB + AD
$= \frac{2}{\sqrt{2}} + 2 \sqrt{2} = \sqrt{2} + 2 \sqrt{2} = 3 \sqrt{2}$

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