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Let equation of L1 be y=x-5 , which has a slope m of 1.
and equation of color(red)(L3) be color(red)(y=-2x-6)
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=1xx2+b, => b=1
=> equation of color(red)(L2) in slope-intercept form is color(red)(y=x+1)
Set the equations of L2 and L3 equal to each other to find the intersection point P
=> x+1=-2x-6, => x=-7/3
=> y=-(7/3)+1=-4/3
=> coordinates of P = (-7/3,-4/3)
The distance from A(2,3) to P(-7/3,-4/3) is
d=sqrt((-7/3-2)^2+(-4/3-3)^2)
=sqrt(338/9)~~6.13 units
