Answer:
[tex](-\frac{3}{8},2)[/tex]
Step-by-step explanation:
Point Z divides XY into a 5:3 ratio, so Z is 5/3 of the way from X to Y. That ratio is k, found by writing the numerator of the ratio (5) over the sum of the numerator and the denominator (5 + 3 = 8). Our k value is 5/8. Now we will find the rise and run values which is the slope of this line segment:
[tex]m=\frac{2-2}{-6-9} =\frac{0}{-15}[/tex]
Coordinates are found in this formula:
[tex]Z(x,y)=(x_{1}+k(run),y_{1} +k(rise))[/tex]
Filling that in:
[tex]Z(x,y)=(9+\frac{5}{8}(-15),2+\frac{5}{8}(0))[/tex]
which simplifies to
[tex]Z(x,y)=(9-\frac{75}{8},2+0)[/tex]
which gives us the final coordinates of Z to be [tex]Z(x,y)=(-\frac{3}{8},2)[/tex]
