Answer:
b.
Step-by-step explanation:
First off, let's name these endpoints. We will call them J(3, -2) and K(8, 0). The point we are looking for that divides this into a 3:1 ratio let's call L. We are looking for point L that divides segment JK into a 3:1 ratio.
A 3:1 ratio means that we need to divide JK into 3 + 1 equal parts, or 4. Point L divides JK into a 3:1 ratio. We need to find the constant of proportionality, k, that can be used in the formula to find the coordinates of L. k is found by putting the numerator of the 3/1 ratio over the sum of the numerator and denominator. Therefore, our k value is 3/4.
Now we need to find the slope of the given segment.
[tex]m=\frac{0-(-2)}{8-3}=\frac{2}{5}[/tex]
The coordinates of L can be found in this formula:
[tex]L(x, y)=(x_{1}+k(run),x_{2}+k(rise))[/tex]
Filling in:
[tex]L(x,y)=(3+\frac{3}{4}(5),-2+\frac{3}4}(2))[/tex]
Simplifying we have:
[tex]L(x,y)=(3+\frac{15}{4},-2+\frac{6}{4})[/tex]
Simplifying further:
[tex]L(x,y)=(\frac{12}{4}+\frac{15}{4},\frac{-8}{4} +\frac{6}{4})[/tex]
And we have the coordinates of L to be
[tex]L(x,y)=(\frac{27}{4},-\frac{1}{2})[/tex]
27/4 does divide to 6.75
