Question

If the point $(x_1+t(x_2-x_1),y_1+t(y_2-y_1\left)\right)$ divides the join of $(x_1,y_1)$ and $(x_2,y_2)$ internally in the ratio $t:1-t$, then

• A. $t<0$
• B. $0<t<1$
• C. $t>1$
• D. $t=1$

Answer 1

The correct option is B $0<t<1$

$(x_1+t(x_2-x_1),y_1+t(y_2-y_1\left)\right)=\left(x_1\right(1-t)+t{x}_2,y_1(1-t)+t{y}_2)$ is the point which divides $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $t:1-t$
Since, the point divides internally

$\therefore$ Ratio must be positive.
$\therefore \frac{t}{1-t}>0$ and $t(1-t)>0$

Thus, $0<t<1.$