GATE2014 AG: GA-9

Question

$X$ is $1$ km northeast of $Y$. $Y$ is $1$ km southeast of $Z$. $W$ is $1$ km west of $Z$. $P$ is $1$ km south of $W$. $Q$ is $1$ km east of $P$. What is the distance between $X$ and $Q$ in km?

• A. $1$ 
• B. $\sqrt{2}$
• C. $\sqrt{3}$
• D. $2$

Comments

no its  root (3) in km

Answer 1

Let's break the whole thing down :

$X$ is $1 \hspace{0.1cm} km$ northeast of $Y$

$Y$ is $1 \hspace{0.1cm} km$ southeast of $Z$.

$W$ is $1\hspace{0.1cm}  km$ west of $Z$

$P$ is $1 \hspace{0.1cm} km$ south of $W$

$Q$ is $1 \hspace{0.1cm} km$ east of $P$

The distance between $X$ & $Z$ will be 

Applying pythagoras theorem on $\triangle XYZ$ triangle, we get-

$(XZ)^2 = (XY)^2+(YZ)^2$

Or, $(XZ)^2 = 1+1$ $\qquad \left [ ∵ XY = 1 \hspace{0.1cm} km \hspace{0.1cm} \& \hspace{0.1cm}YZ = 1 \hspace{0.1cm}  km \right ]$

Or, $XZ = \sqrt{2} \hspace{0.1cm} km$

Now, we need to find the distance between $X$ & $Q$ in km

By applying Pythagoras Theorem on $\triangle XQZ$ we get -

$(XQ)^2 = (QZ)^2+(ZX)^2$

Or, $(XQ)^2 = 1^2 + (\sqrt{2})^2$  $\qquad \left[ ∵ QZ = 1\hspace{0.1cm} km \hspace{0.1cm} \& \hspace{0.1cm} ZX = \sqrt{2} \hspace{0.1cm}  km\right ]$

Or, $(XQ)^2 = 1+2 = 3$

Or, $(XQ) = \sqrt{3} \hspace{0.1cm} km$

Correct Answer: $C$

Comments

Incredible ans

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good one !!

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shouldn’t we take X to Y distance i.e. the distance of line as 1 Km ??

Answer 2

Answer : $\sqrt{3}$ km.

Comments

nice explanation :)

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thanxxx

Answer 3

distance between XQ is $√$$($1² +$(√2)$²)$ =√3$

Answer 4

Answer is root 3 km.
ps- PT is pythogoras theorem

 

Comments

Thanks for the explaination.