GATE Civil 2021 Set 2 | GA Question: 6

Question

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 $Q$ that is $8$ units North of point $P$.
The distance of point $Q$ to point $O$, in the same units, should be ______________

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

First, we can draw the diagram using the given description.

$\triangle ODQ$ is right angle triangle, so here we can apply Pythagoras's theorem, then we get

$OQ^{2} = OD^{2} + DQ^{2}$

$\implies OQ^{2} = 4^{2} + 3^{2} = 16 + 9 = 25$

$\implies OQ= 5$ units.

$\therefore$ The distance of point $Q$ to point $O,$ in the same units, should be $5.$

So, the correct answer is $(C).$