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-
Let equation of L1 be y=x−5 , which has a slope m of 1.
and equation of L3 be 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=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=−2x−6,⇒x=−73
⇒y=−(73)+1=−43
⇒ coordinates of P=(−73,−43)
The distance from A(2,3) to P(−73,−43) is
d=√(−73−2)2+(−43−3)2
=√3389≈6.13 units
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Oct 24, 2024 Last updated |
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