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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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detailed solution

Correct option is B

(x1+t(x2−x1),y1+t(y2−y1))≡(x1(1−t)+tx2,y1(1−t)+ty2) is the point which divides the join of (x1,y1) and (x2,y2) in the ration t:(1−t),which is positive if 0

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If the point (x1+t(x2−x1),y1+t(y2−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