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Solution for Parallel to the line - JEE PDF Download

Find distance of point A(2,3) measured parallel to the line x- y=5 from the line 2x+y+6=0.?
Ref: https://edurev.in/question/616992/Find-distance-of-point-A-2-3-measured-parallel-to-the-line-x-y5-from-the-line-2xy60-

Solution for Parallel to the line - JEE

Let equation of L1 be y=x5 , which has a slope m of 1.
and equation of L3 be y=2x6
Draw a line from A(2,3), parallel to L1, to meet L3 at P, as shown in the figure.
AP is the distance measured parallel to L1 from L3
Let the line joining A and P be L2.
Given that L2 is parallel to L1,
L2 has the same slope (m=1) as that of L1,

Now find the equation of L2 through A(2,3) with a slope of m=1.
y=mx+b
3=1×2+b,b=1
equation of L2 in slope-intercept form is y=x+1
Set the equations of L2andL3 equal to each other to find the intersection point P
x+1=2x6,x=73
y=(73)+1=43
coordinates of P=(73,43)

The distance from A(2,3) to P(73,43) is
d=(732)2+(433)2
=33896.13 units

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