On a planar field, you travelled 3 units East from a point O. Next you travelled 4 units South to arrive at point P. Then you travelled from P in the North-East direction such that you arrive at a point that is 6 units East of point O. Next, you travelled in the North-West direction, so that you arrive at point Q. The distance of point Q to point O (in the same units) should be
A. 3
B. 4
C. 5
D. 6
GATE 2021 · General Aptitude · Direction Sense · medium
Answer: OQ = 5 units. Answer: C.
Assign coordinates to each waypoint: O = (0, 0). After 3 East: (3, 0). After 4 South: P = (3, -4). NE from P means equal x and y increments. To reach x = 6 (6 units East of O): delta_x = 3, so delta_y = 3 (NE is 45 deg). Intermediate point R = (3+3, -4+3) = (6, -1).
Find Q on the NW ray from R and compute OQ: NW from R=(6,-1): subtract t from x and add t to y, giving Q = (6-t, -1+t). Distance OQ = sqrt((6-t)^2 + (t-1)^2) = sqrt(2t^2 - 14t + 37). Setting this equal to 5: 2t^2 - 14t + 12 = 0, so t^2 - 7t + 6 = 0, giving t = 1 (Q = (5,0)) or t = 6 (Q = (0,5)). Both give OQ = 5.