Question

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 locus of `t` is
A. tlt0
B. 0lttlt1
C. tgt1
D. t=1

Answer 1

Correct Answer - B
`(x_(1)+t(x_(2)-x_(1)),y_(1)+t(y_(2)-y_(1)))`
`=(x_(1)(l-t)+tx_(2),y_(1)(l-t)+ty_(2))` is the point which divides the join of `(x_(1) ,y_(1))` and `(x_(2), y_(2))` in the ratio t : (l-t) which is positive if `0lt tlt 1`