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STRAIGHT LINES
Asked by devendra.mittal | 05 Jan, 2010, 10:01: PM Expert Answer

To find reflection of line x+y+1=0 in the line 2x+y+1=0.

Slope of the reflected line will be same in magnitude but opposite in sign to the  line i.e x+y+1 =0

so slope of required line is  1.....(i) Consider a point on the line (x+y+1)=0 say (1,-2)  now this point is reflected in the line 2x+y+1=0, let its  image be (h,k)

Mid point of line joining (1,-2) and (h,k)  is (h+1)/2, (k-2)/2

This mid point lies on line 2x+y+1 =0  so it must satis fies the equation of  line

2(h+1)/2+(k-2)/2+1=0 i.e h+1+k/2=0.....(ii)

Also the line joining (1,-2) and (h,k)  is perpendicular to the line 2x+y+1=0

so thiir slopes are negative reciprocal of each other

(k+2)/(h-1)=1/2 solving gives us

2k-h+5=0...(iii)

Solving  (ii) and (iii) we get h=1/5 and k=-12/5

Equation of  reflected line will be x-1/5=1(y+12/5) using (i)

5x-1=5y+12

or 5x-5y =13

Answered by | 08 Jan, 2010, 11:25: AM
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