Answer: [tex]\left(\dfrac{-7}{2},\dfrac{5}{4}\right)[/tex].
Step-by-step explanation:
It is given that Point A is at (-5, -4) and point B at (-3, 3).
We need to find the coordinates of the point which is 3/4 of the way from A to B.
Let the required point be P.
[tex]AP:AB=3:4[/tex]
[tex]AP:PB=AP:(AB-AP)=3:(4-1)=3:1[/tex]
It means, point P divides segment AB in 3:1.
Section formula: If a point divides a line segment in m:n, then
[tex]\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
Using section formula, we get
[tex]P=\left(\dfrac{3(-3)+1(-5)}{3+1},\dfrac{3(3)+1(-4)}{3+1}\right)[/tex]
[tex]P=\left(\dfrac{-9-5}{4},\dfrac{9-4}{4}\right)[/tex]
[tex]P=\left(\dfrac{-14}{4},\dfrac{5}{4}\right)[/tex]
[tex]P=\left(\dfrac{-7}{2},\dfrac{5}{4}\right)[/tex]
Therefore, the required point is [tex]\left(\dfrac{-7}{2},\dfrac{5}{4}\right)[/tex].
