First slide

Cartesian plane

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

Easy

A

t<0
B

0<t<1
C

t>1
D

t=1

Solution

$(x_{1} + t (x_{2} - x_{1}), y_{1} + t (y_{2} - y_{1})) \equiv (x_{1} (1 - t) + {tx}_{2}, y_{1} (1 - t) + {ty}_{2})$ is the point which divides the join of $(x_{1}, y_{1}) and (x_{2}, y_{2})$ in the ration $t : (1 - t),$ which is positive if $0 < t < 1$ .

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