Question

What are the coordinates of the point 3/4 of the way from A to B

Answer 1

The first thing we have to do is find the distance between points A and B for that we use the following equation

$D_{AB}=\sqrt[]{(x_A-x_B)^2+(y_A-y_B)^2}$

From the graph we identify our points A and B and substitute to find their distance

$\begin{gathered} (-5,-4)\to A \\ (-3,3)\to B \\ D_{AB}=\sqrt[]{(-5_{}-(-3)_{})^2+(-4_{}-3_{})^2} \\ D_{AB}=\sqrt[]{53} \end{gathered}$

To calculate any point between 2 points we use the following equations

$\begin{gathered} r=\frac{3}{4} \\ x_p=\frac{x_A+r\cdot x_B}{1+r} \\ x_p=\frac{-5_{}+(\frac{3}{4})\cdot(-3)}{1+\frac{3}{4}} \\ x_p=-4.1428 \end{gathered}$$\begin{gathered} r=\frac{3}{4} \\ y_p=\frac{y_A+r\cdot y_B}{1+r} \\ y_p=\frac{-4_{}+(\frac{3}{4})(3)}{1+\frac{3}{4}} \\ y_p=-1 \end{gathered}$

The coordinates of the point 3/4 between A and B are

$(-4.14,-1)$