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$If the point (x_{1} + t (x_{2} - x_{1}), y_{1} + t (y_{2} - y_{1})) divides the join of (x_{1}, y_{1}) and (x_{2}, y_{2}) internally, then$

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t<0

t>1

t=1

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Correct option is B

x coordinate of the point x1+tx2−x1,y1+ty2−y1 can be rewrite as x1+tx2-tx11=x11-t+tx2t+1-tthis gives the x -coordiante of a point which divides the line segment joining the given points in the ratio t:1-t internallyhere 1-t>0⇒t<1

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If the point x1+tx2−x1,y1+ty2−y1 divides the join of x1,y1 and x2,y2 internally, then

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$If the point (x_{1} + t (x_{2} - x_{1}), y_{1} + t (y_{2} - y_{1})) divides the join of (x_{1}, y_{1}) and (x_{2}, y_{2}) internally, then$