Question

Aju was standing at the corner of a square field. He started walking towards North-East direction. When he was $10\sqrt{2}$ m away from where he started, he took a left turn and started walking again. Considering the square field as the coordinate plane and starting point as the origin, find the equation of Aju’s current path.

Answer 1

AB = $10\sqrt{2}$m

Since Aju travelled towards North - East direction, he makes an angle of ${45}^{\circ }$ with the x -axis.

$\therefore$ coordinates of point B = (10, 10)

Equation of AB (whose Slope is 1 and passing through origin) : x – y = 0

After a left turn, the new path will be perpendicular to the initial path.

$\therefore$ slope of the new path = -1 [as the lines are perpendicular]

Equation of line whose slope is -1 and passing through (10,10) is

$(y-y_1)=m(x-x_1)$

$(y-10)=(-1)(x-10)$

$\Rightarrow x+y=20$