# 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 –

**Solution: **

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

i-e;

Here

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;

**So, you will be 2.82 km from your start point**