Question

The point which divides the line segment joining $(-2,4),(2,7)$ in the ratio $2:1$ externally is

• A. $(6,10)$
• B. $(2,\frac{10}{3})$
• C. $(\frac{-4}{3},\frac{2}{3})$
• D. $(\frac{2}{3},6)$

Answer 1

The correct option is A $(6,10)$

REF.Image.

$A(-2,4)B(2,7)$

$x_1{y}_1$ $x_2{y}_2$

$m_1:m_2=2:1$

$P(x,y)=(\frac{m_1{x}_2-m_2{x}_1}{m_2-m_2},\frac{m_1{y}_2-m_2{y}_1}{m_1-m_2})$

$x=\frac{m_1{x}_2-m_2{x}_1}{m_1-m_2}=\frac{2\left(2\right)-1(-2)}{2+(-1)}=4+2=6$

$y=\frac{m_1{y}_2-m_2{y}_1}{m_1-m_2}=\frac{2\left(7\right)-1\left(4\right)}{2-1}=14-4=10$

$\therefore P(x,y)=(6,10).$