Question

Given the points A(-1,2) and B(7,10), find the coordinates of the point P on the directed line segment AB that partitions AB into ratio 1:3. What is the answer for point P?

Answer 1

A = (-1, 2)

B = (7, 10)

1:3

Formula

$\begin{gathered} \text{ x = }\frac{x1\text{ + rx2}}{1\text{ + r}} \\ \text{ y = }\frac{y1\text{ + ry2}}{1\text{ + r}} \end{gathered}$

Substitution

$\text{ x = }\frac{-1\text{ + }\frac{1}{3}\text{(7)}}{1\text{ + }\frac{1}{3}}\text{ = }\frac{-1\text{ + }\frac{7}{3}}{\frac{3\text{ + 1}}{3}}\text{ = }\frac{\frac{-3\text{ + 7}}{3}}{\frac{3\text{ + 1}}{3}}\text{ = }\frac{\frac{4}{3}}{\frac{4}{3}}\text{ = 1}$$\text{ y = }\frac{2\text{ + }\frac{1}{3}(10)}{1\text{ + }\frac{1}{3}}\text{ = }\frac{2\text{ + }\frac{10}{3}}{\frac{3\text{ + 1}}{3}}\text{ = }\frac{\frac{6\text{ + 10}}{3}}{\frac{4}{3}}\text{ = }\frac{16}{4}\text{ = 4}$

Result x = 1, y = 4