2 votes

Fatima starts from point $P$, goes North for $3$ km, and then East for $4$ km to reach point $Q$. She then turns to face point $P$ and goes $15$ km in that direction. She then goes North for $6$ km. How far is she from point $P$, and in which direction should she go to reach point $P$?

- $\text{8 km, East}$
- $\text{12 km, North}$
- $\text{6k m, East}$
- $\text{10 km, North}$

Migrated from GO Electronics 1 year ago by Arjun

4 votes

Best answer

5

After travelling 6km from y to z how can we assume that z is on straight line from p to z??

Iam stuck here

Iam stuck here

4

In $\Delta QPX \:\text{&}\:\Delta PYZ$,

$\frac{QP}{PY}=\frac{PX}{YZ}=\frac{1}{2}$

&, $\angle QPX=\angle PYZ$ {$\because$ corresponding angles of two parallel lines XP & ZY}

$\therefore$ $\Delta QPX \:\text{&}\:\Delta PYZ$ are similar (from $\text{SAS}$ similarity).

thus, angles of similar triangles are same.

So, $\angle YZP=\angle PXQ = 90^\circ$

Also, similar triangles have proportional sides,

so, $\frac{QP}{PY}=\frac{PX}{YZ}=\frac{XQ}{ZP}$

=>$\frac{XQ}{ZP}=\frac{1}{2}$

=> $ZP=8\:Km$.