Question

If the point $P(1,2)$ lies on line segment joining the points $A(2,4)$ and $B(4,8)$ then find $\frac{AP}{AB}$.

Answer 1

we have: $P(1,2)$, $A(2,4)$, $B(4,8)$

Distance formula we have,

$D=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

$AP=\sqrt{(2-1{)}^2+(4-2{)}^2}=\sqrt{5}$

$AB=\sqrt{(2-4{)}^2+(4-8{)}^2}=2\sqrt{5}$

$\Rightarrow \left(\frac{AP}{AB}\right)=\frac{1}{2}$.