The coordinates of the point 3/4 of the way from A to B is [tex]\left(-\frac{7}{2},\frac{5}{4} \right)[/tex].
In this question we have a line segment whose endpoints are known, the most compact approach to determine the location of a point C so that it is 3/4 of the way from A to B is determined by the following vectorial formula:
[tex]\vec C = \vec A + r\cdot (\vec B - \vec A)[/tex] (1)
Where [tex]r[/tex] is the distance ratio.
If we know that [tex]\vec A = (-5, -4)[/tex], [tex]\vec B = (-3, 3)[/tex] and [tex]r = \frac{3}{4}[/tex], then the coordinates of point C is:
[tex]\vec C = (-5, -4) + \frac{3}{4}\cdot [(-3, 3) - (-5,-4)][/tex]
[tex]\vec C = (-5, -4) + \frac{3}{4}\cdot (2, 7)[/tex]
[tex]\vec C = (-5,-4) + \left(\frac{3}{2}, \frac{21}{4} \right)[/tex]
[tex]\vec C = \left(-\frac{7}{2},\frac{5}{4} \right)[/tex]
The coordinates of the point 3/4 of the way from A to B is [tex]\left(-\frac{7}{2},\frac{5}{4} \right)[/tex].
We kindly invite to see this question on line segments: https://brainly.com/question/12282593
