If the point `x_1+t(x_2-x_1),y_1+t(y_2-y_1)` divides the join of `(x_1,y_1)` and `(x_2,y-2)` internally then

Options

A. `t lt 0`
B. `0 lt t lt1`
C. `t lt1`
D. `t=1`

Answer

B

Explanation

The co-ordinates of the points of division are
`(x_(1)+t(x_(2)-x_(1)),y_(1)t(y_(2)=y_(1)))`
`=(((1-t)x_(1)+tx_(2))/((1-t)+t)=((1-t)y_(1)+ty_(2))/((1-t)+t))`
Clearly, these are the coordinates of the point dividing the join of `(x_(1),y_(1)) and (x_(2),y_(2))` in the ratio `t:(1-t)`
For the internal division, we must have
`tgt0 and 1-t0 rArr 0 lt t lt 1`