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)`

Coordinates of P ` = ((6m_(1) -4m_(2))/(m_(1)+m_(2)) , (-5m_(1) +7m_(1))/(m_(1)+m_(2)))`
Since the point P lies on the line
2x + 5y -7=0
` 2((6m_(1)-4m_(2))/(m_(1)+m_(2))) + 5((-5m_(1) +7m_(2))/(m_(1) + m_(2))) -7=0`
`Rightarrow 12m_(1) -8m_(2) -25m_(1) +35m_(2)-7m_(1) -7m_(2)=0`
` Rightarrow -20m_(1)+20m_(2)=0`
`Rightarrow m_(1) =m_(2)`
`Rightarrow m_(1)/m_(2) =1/1`
` therefore m_(1):m_(2)=1:1`