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The distance of a point (2,3) from the ...

The distance of a point (2,3) from the line 2x -3y + 9 = 0 measured along a line x-y +1 =0 is :

A

4

B

`2sqrt(2)`

C

`8sqrt(2)`

D

`4sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
The slope of the line `x-y+1=0`. So, it makes and angle of `45^(@)` with x-axis.
The equation of a line passing through (2,3) and making an angle of `45^(@)` is given by
`(x-2)/(cos 45^(@))=(y-3)/(sin 45^(@))=r`
Co-ordinate of any point on his line are ltbr? `(2+r cos 45^(@), 3+r sin 45^(@))` or, `(2+(r)/(sqrt(2)),3+(r)/(sqrt(3)))`
If this point lies on the line `3=2x-3y+9=0`
`4+rsqrt(2)-9-(3r)/(sqrt(2))+9=0 implies r=4sqrt(2)` units.
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