Straight Lines
Straight Line
Allen Star Batch
Grade 11
Question:
Two roads are represented by the equation $y - x = 6$ and $x + y = 8$. An inspection bunglow has to be so constructed that it is at a distance of 100 from each of the roads. Possible location of the bunglow is given by:
$\left(100\sqrt{2} + 1.7\right)$
$\left(1 - 100\sqrt{2}.7\right)$
$\left(1.7 + 100\sqrt{2}\right)$
$\left(1.7 - 100\sqrt{2}\right)$
Step-by-Step Solution
Key Concept: Points equidistant from two lines lie on their angle bisectors, and the perpendicular bisector distance determines the square's size.
Four points equidistant from two given lines form a square. Given lines are $y - x = 6$ and $x + y = 8$, which are perpendicular. The four equidistant points lie on the angle bisectors of these lines. The square has side length $200$ and diagonal length $200\sqrt{2}$. The coordinates are $D = [1 + 100\sqrt{2}, 7]$, $A = [1.7 + 100\sqrt{2}]$, $B = [1 - 100\sqrt{2}, 7]$, and $C = [1.7 - 100\sqrt{2}]$.
Correct Answer: 1,2,3,4