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

Result x = 1, y = 4