Question

If A and B are (– 2, – 2) and (2, – 4) respectively; then find the co-ordinates of the point P such that ${\displaystyle \frac{AB}{AB}=\frac{3}{7}}$.

Answer 1

${\displaystyle \frac{AP}{AB}=\frac{3}{7}}$

∴ ${\displaystyle \frac{AP}{PB}=\frac{3}{4}}$

${\displaystyle P(\frac{m_1{x}_2+m_2{x}_1}{m_1+m_2},\frac{m_1{y}_2+m_2{y}_1}{m_1+m_2})}$

= ${\displaystyle \frac{3\times 2+4(-2)}{3+4},\frac{3\times -4+4\times \left(2\right)}{3+4}}$

= ${\displaystyle (\frac{-2}{7},\frac{4}{7})}$