Straight LineHardBloom L6
Question
On the portion of the straight line, $x + 2y = 4$ intercepted between the axes, a square is constructed on the side of the line away from the origin. Then the point of intersection of its diagonals has co-ordinates :
Options
A.$(2,3)$
B.$(3,2)$
C.$(3,3)$
D.$(2,2)$
Solution
Sol. [Key Concept: Square built on the far side of an intercept segment: its diagonal-intersection is the segment midpoint shifted outward by half a diagonal.]
Slope of $PQ = 2 = tan\theta$
$$\begin{matrix} P & \ \equiv \left( 2 + \sqrt{5} \cdot \frac{1}{\sqrt{5}},1 + \sqrt{5} \cdot \frac{2}{\sqrt{5}} \right) \\ & \ = (3,3) \end{matrix}$$
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