Question

If $A(-4,3)$, $B(5,7)$, then the point on the line segment $AB$ which is two thirds away from $A$ to $B$ is

• A. $(2,\frac{17}{3})$
• B. $(2,6)$
• C. $(2,5)$
• D. $(2,\frac{11}{3})$

Answer 1

The correct option is A $(2,\frac{17}{3})$

Let $P$ be the required point,
$AP=\frac{2}{3}AB\Rightarrow PB=\frac{1}{3}AB\Rightarrow \frac{AP}{PB}=\frac{2}{1}\Rightarrow P=(\frac{10-4}{3},\frac{14+3}{3})\therefore P=(2,\frac{17}{3})$