Answer :
Answer:
The coordinates of K is (-5,1)
Step-by-step explanation:
Given
[tex]J = (-9,-5)[/tex]
[tex]L = (5,16)[/tex]
[tex]JK:KL = 2:5[/tex]
Required
Determine K
Using Line ratio formula;
We have:
[tex]K(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
Where
[tex](x_1,y_1) = (-9,-5)[/tex]
[tex](x_2,y_2) = (5,16)[/tex]
[tex]m:n = 2:5[/tex]
So; we have:
[tex]K(x,y) = (\frac{2 * 5 + 5 * -9}{2+5},\frac{2 * 16 + 5 * -5}{2+5})[/tex]
[tex]K(x,y) = (\frac{10 -45}{7},\frac{32 -25}{7})[/tex]
[tex]K(x,y) = (\frac{-35}{7},\frac{7}{7})[/tex]
[tex]K(x,y) = (-5,1)[/tex]