Find the distance between the lines 4x-3y+5=0 and 8x-6y+7=0..

Asked by Suryavanshikatoch | 11th Feb, 2019, 07:37: PM

Expert Answer:


 lines 4x-3y+5=0 and 8x-6y+7 =0 are parallel lines with slope 4/3 as shown in figure.

Point of intersection of both lines with y-axis is obtained by substituting x=0 in the equations.
 
Points of intersection A (0, 5/3) and B(0,7/6) are shown in figure.
 
Perpendiculr line to both the lines is in the form 3x+4y = k . This perpendicular line passes through A(0, 5/3)
by substituting values for x and y in the equation we get k = 20/3
 
point of intersection is obtained by solving the equations 8x-6y+7=0  and 3x+4y = (20/3)
 
we get point of intersection as C ( 0.24, 1.5)
 
distance between the lines = begin mathsize 12px style square root of open parentheses 0.24 close parentheses squared plus open parentheses 0.16 close parentheses squared end root space almost equal to space 0.29 end style
 

Answered by Thiyagarajan K | 11th Feb, 2019, 10:24: PM

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