Aju was standing at the corner of a square field. He started walking towards North-East direction. When he was 10√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.
Aju was standing at the corner of a square field. He started walking towards North-East direction. When he was 10√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.
The correct option is B x + y – 20 = 0
AB = 10√2m
Since Aju travelled towards North - East direction, he makes an angle of 45∘ with the x -axis.
∴ 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.
∴ 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−y1) = m(x−x1)
(y−10) = (−1)(x−10)
⇒x+y=20
x + y – 20 = 0
AB = 10√2m
Since Aju travelled towards North - East direction, he makes an angle of 45∘ with the x -axis.
∴ 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.
∴ 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−y1) = m(x−x1)
(y−10) = (−1)(x−10)
⇒x+y=20
