﻿ A straight canal is at a distance of  km from a city and the nearest path from the city to the canal is in the north-east direction. Find whether a village which is at 3 km north and 4 km east from the city lies on the canal or not. If not, then on which side of the canal is the village situated?  : Kaysons Education

# A Straight Canal Is At A Distance Of  km From A City And The Nearest Path From The City To The Canal Is In The North-east Direction. Find Whether A Village Which Is At 3 Km North And 4 Km East From The City Lies On The Canal Or Not. If Not, Then On Which Side Of The Canal Is The Village Situated?

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## Question

### Solution

Correct option is

Let O(0, 0) be the given city and AB be the straight canal.

∴ Equation of AB

i.e., Equation of canal is

Let V be the given village, then V ≡ (4, 3)

Putting x = 4 and y = 3 in (i), then

Hence the given village V does not lie on the canal. Also if,

.

Hence the village is on that side of the canal on which origin or city lies.

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