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Mathematics Question on Straight lines

Suppose the line mx-y+ 5m-4=0 meets the lines x+3y+2=0, 2x+3y+4=0 and x-y-5=0 at the points R. S and T, respectively. If R, S and T are at distances r1, r2 and r3, respectively, from (-5,-4) and (15r1)2+(10r2)2=(6r3)2(\frac{15}{r_1})^2+(\frac{10}{r_2})^2=(\frac{6}{r_3})^2 then the value of m is

A

−23\frac{-2}{3}

B

23\frac{2}{3}

C

32\frac{3}{2}

D

−32\frac{-3}{2}

E

1

Answer

−23\frac{-2}{3}

Explanation

Solution

The correct option is (A): −23\frac{-2}{3}