Question

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

Answer 1

Statement Problem: What are the coordinates of the point 3/4 of the way from A to B in the plotted graph?

Solution:

The coordinates of point A and B respectively is;

`A(-5,-4),B(-3,3)`

The midpoint of the line segment AB is;

`\begin{gathered} \text{Midpoint = (}(x_1+x_2)/(2),(y_1+y_2)/(2)) \\ x_1=-5,y_1=-4,x_2=-3,y_2=3 \\ \text{Midpoint}=\text{ (}(-5+(-3))/(2),(-4+3)/(2)) \\ \text{Midpoint}=(-(8)/(2),-(1)/(2)) \\ \text{Midpoint}=(-4,-0.5) \end{gathered}`

The coordinates of the point 3/4 of the way from A to B is the midpoint of the midpoint of line AB to B. That is;

`\begin{gathered} M(-4,-0.5),B(-3,3) \\ \text{midpoint}=((-4+(-3))/(2),((-0.5+3)/(2)) \\ \text{Midpoint}=(-(7)/(2),(2.5)/(2)) \\ \text{Midpoint}=(-3.5,1.25) \end{gathered}`

The required coordinates of the point 3/4 of the way from A to B is;

`(-3.5,1.25)`