The distance of the point (1,3) from the line 2x−3y+9=0 measured along a line x−y+1=0
A
2√2
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B
3√2
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C
4√2
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D
4√2
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Solution
The correct option is A2√2
Let the point be P, lines be L1 & L2 and ′d′ be the distance of point P(1,3) from the line L1 along the direction of line L2
Let the line segment from point P intersect line L1 at O
⇒ slope of L2= slope of OP L2:y=x+1 ⇒ slope of L2=1 ⇒ slope of OP=1
we have slope of OP and point P(1,3)
Equation of OP will be y=x+2...(1) L1:2x−3y+9=0...(2)
Coordinates of O can be obtained from eqn (1) and (2) O=(3,5)