Word Problem 4

Problem 4: You started from a place and went 4 km north and turned left and moved 2 km west. Then you again turned left and moved 2 kms. How many kilometers are you from the place you started ?

a. 4km        b. 2km           c. 6km               d. 10 km

— end point  and start point mathematics, ray math definition


We draw path as below





Let S be the start point and first movement is from point S to point B – 4 kms in the north direction. At point B you turned left (west) and moved 2 kms and reached point C. Then you turned left again (South) and reached point E.

If we join point E to the line SB then it will touch it at point A – which is mid of the way S to B. So, A to B will be of 2 km length as well.

We join point E with S by a double line. We have to find the length of this double line which will be the distance of your last location E from the start point S.

Clearly here S to A to E is a right angled triangle !

We use Pythagoras Theorem to find the length E to S


 (SA)^{2}+(AE) ^{2}=(ES) ^{2}


SA=2 (because A is mid of 4 km line SB)

AE=2 (because EA is parallel to BC line and equal in length)

Put values in expression;

 (2)^{2}+(2) ^{2}=(ES) ^{2}

 4+4=(ES) ^{2}

\Rightarrow ES= \sqrt{8}

\Rightarrow ES= 2\sqrt{2}=2.82 km



So, you will be 2.82 km from your start point








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