Line formed by (-4,7)&(6,-5) is y-y`=m(x-x`)y-7= -6÷5(x+4)6x+5y-11=0The intetsection between the lines 2x+5y-7=0&6x+5y-11=0 is3×(2x+5y-7)=0=》6x+15y-21=0____(1) 6x+5y-11=0_______(2) (1) - (2)=》10y-10=010y=10y=1Substitute y=1 in (1) ,we get6x+15(1)-21=06x=6x=1So point of intersection of the two lines is (1,1)This point divides the line in some ratio.Let the point divides the line in the ratio m:nBy section formula , the point that divides the line segment joining the points (x,y) & (x`,y`) in the ratio m:n is (mx`+nx÷m+n),(my`+ny÷m+n)That is,[(m(6)+n(-4)÷m+n),(m(-5)+n(7)÷m+n)]=[1,1]Comparing any respective coordinates abcissae or ordinate, we get,(6m-4n)÷m+n=16m-4n=m+n5m=5nm=nm÷n=1That is m:n=1:1
