Maths · Distance formula, sections formula, locus and its equation

If the point , \boldsymbol{y}_{1}+\right. \) \right) \) divides the join of \) a

If the point \( \left(\boldsymbol{x}_{1}+\boldsymbol{t}\left(\boldsymbol{x}_{2}-\boldsymbol{x}_{1}\right), \boldsymbol{y}_{1}+\right. \) \( \left.t\left(y_{2}-y_{1}\right)\right) \) divides the join of \( \left(x_{1}, y_{1}\right) \) and \( \left(x_{2}, y_{2}\right) \) internally, then

  • A. \( t<0 \)
  • B. \( 0<t<1 \)
  • C. \( t>1 \)
  • D. \( t=1 \)

Step-by-step solution

The point (x1 + t(x2 - x1), y1 + t(y2 - y1)) is a parametric representation of the line segment joining (x1,y1) and (x2,y2). For internal division, the parameter t must satisfy 0 < t < 1, with t=0 giving the first endpoint and t=1 the second.
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