Question

What are the coordinates of the point that lies of the way along directed line segment AB with A(2,5) and B(14,9)?

Answer 1

1/4 of the distance between points A(2,5) and B(14,9) is given by the formula:

`\begin{gathered} (1)/(4)AB=(1)/(4)\sqrt[]{(x_2-x_1)^2+(y_2}-y_1)^2 \\ (1)/(4)AB=(1)/(4)\sqrt[]{(14-2)^2+(9-5)^2} \\ (1)/(4)AB=(1)/(4)\sqrt[]{12^2+4^2}\text{ = }(1)/(4)\sqrt[]{144+16} \\ (1)/(4)AB=(1)/(4)\text{ }\sqrt[]{160}=(1)/(4)*12.649=3.162 \end{gathered}`