Question

Given a directed line segment AB with coordinates A(x1, y₁) and B(x2, y2),

if point P partitions AB such that the ratio of AP to AB is k,
then the coordinates of P are:
*Important: The ratio must be written as a part to whole in fraction form!

Answer 1

Hi,

Explanation:

`\overrightarrow{OA}=x_1*\vec{i}+y_1*\vec{j}\\\\\overrightarrow{OB}=x_2*\vec{i}+y_2*\vec{j}\\\\\frac{\overrightarrow{AP}}{\overrightarrow{AB}}=k \\\\\overrightarrow{OP}=\overrightarrow{OA}+\overrightarrow{AP}\\=x_1*\vec{i}+y_1*\vec{j}+k*\overrightarrow{AB}\\=x_1*\vec{i}+y_1*\vec{j}+k*(x_2-x_1)*\vec{i}+k*(y_2-y_1)*\vec{j}\\=(x_1+k(x_2-x_1))*\vec{i}+(y_1+k(y_2-y_1))*\vec{j}\\\\\boxed{P=(x_1+k(x_2-x_1),(y_1+k(y_2-y_1) )}`