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# a)) show that the distance d between the parallel lines Ax+By+C1=0 and Ax+By+C2=0 in the plane is :d=l C1 - C2 l/ $\sqrt{\ } \!\,$A^2 + B^2b)) use this result to find the distance between the parallel lines 2x+3y+17=0  and 4x+6y+31=0

10 years ago

see here the lines are

Ax+By+C1=0 say it is  (L 1}  and

Ax+By+C2=0   say it is {L2}  CONSIDER A POINT P{X1,X2} ON L2 AND

SUBSTITUTING THE POINT IN L2 WE GET  WE GET {Ax1+Bx2+c2=0}

we get

Ax1+Bx2=-c2 {minus c2} =1

distance between parallel lines=perpendicular distance from p to (L1)  from 1

Ax+By+C1/root over a2+b2=c1-c2/root over a2=b2

B}

distance between the parallel lines 2x+3y+17=0  and 4x+6y+31=0 =a are multiply by 2 on both sides the equation

2x+3y+17=0 we get 4x+6y+34=0 =b from a and b we get 34-31/root over 4square+6square we get

3/ $\sqrt{\ } \!\,$52

A

=