A straight canal is `4 1/2m i l e s` from a place and the shortest route from this place to the canal is exactly north-east. A village is `3m i l e s` north and four miles east from the place. Does it lie by the nearest edge of the canal?

Explanation

Let the given place be O which is at the origin.let the east and the north directions be x-axis and y-axis respectively

Now, the x cordinate be `(4,0)`(since east) and y cordinate be `(0,3)`since north..the village lies at the point` (4,3)`.


let p be the distance of the canal from the origin (perpendicular dist.,since shortest route)


so,by the normal form of a line


`xcos45^@`+`ysin45^@=p(4.5) `------1)this is the equation of the canal

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