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The ratio by which the line 2x + 5y - 7 = 0 divides the straight line joining the points (-4, 7) and (6, -5) is 1:1 1:4 1:2 2:3

Sai
11 Points
3 years ago
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
ASh
62 Points
3 years ago
In 1st case(-4,7) ,
2x+5y-7=0
=>2(-4)+5(7)-7=0
=>-8+35-7=0
=>20..........(i)
In 2nd case(6,-5) ,
2x+5y-7=0
=>2(6)+5(-5)-7=0
=>12-25-7=0
=>-20.............(¡¡)
by dividing (¡) from (¡¡):
=-20/20
=1/1
RATIO=1:1
I HOPE IT HELPS U!! ^_^ ^_^
◆_◆ PLZZ MARK MY ANSWER AS BRAINLIEST PLZZ ●_●

Sai
11 Points
3 years ago
Is -20/20=1. 1st method is correct.Dont give silly answers