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

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

`(-4.14,-1)`