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

Options

A. `1:4`
B. `1:2`
C. `1:1`
D. `2:3`

Answer

C

Explanation

Let the given line divides the line joining two points in the ratio `m_(1):m_(2)`.

`therefore` Coordinates of P
`=((6m_(1)-4m_(2))/(m_(1)+m_(2)),(-5m_(1)+7m_(2))/(m_(1)+m_(2)))`
since, the point P lies on the line
`2x+5y-7=0`
`therefore2((6m_(1)-4m_(2))/(m_(1)+m_(2)))`
`+5((-5m_(1)+7m_(2))/(m_(1)+m_(2)))-7=0`
`implies12m_(1)-8m_(2)-25m_(1)+35m_(2)-7m_(1)-7m_(2)=0`
`implies-20m_(1)+20m_(2)=0impliesm_(1)=m_(2)`
`implies(m_(1))/(m_(2))=(1)/(1)`
`thereforem_(1):m_(2)=1:1`