[tex] \boxed{(6, -3)} [/tex]
Step-by-step explanation:
Given the ratio 5:3
and Points A and B where A is located at (-6, 3), and B is located at (26, -13).
Let point A be [tex] (x_{1}, y_{1}) [/tex], and let point B be [tex] (x_{2}, y_{2}) [/tex].
(-6, 3) → [tex] (x_{1}, y_{1}) [/tex].
(26, -13) → [tex] (x_{2}, y_{2}) [/tex].
Let 5 be n, and 3 be m.
5:3 → n:m
[tex] (\frac{nx_{1} + mx_{2}}{n+m}, \frac{ny_{1} + my_{2}}{n + m}) [/tex].
To solve, just substitute these variables into the expressions of these coordinates to get the answer.
[tex] (\frac{nx_{1} + mx_{2}}{n+m}, \frac{ny_{1} + my_{2}}{n + m}) [/tex] →
[tex] (\frac{(5)x_{1} + (3)x_{2}}{(5)+(3)}, \frac{(5)y_{1} + (3)y_{2}}{(5) + (3)}) [/tex] →
[tex] (\frac{(5)(-6)+ (3)(26)}{(5)+(3)}, \frac{(5)(3)+ (3)(-13)}{(5) + (3)}) [/tex] →
[tex] (\frac{-30 + 78}{8}, \frac{15+ -39}{8}) [/tex] →
[tex] (\frac{78 – 30}{8}, \frac{15 – 39}{8}) [/tex] →
[tex] (\frac{48}{8}, \frac{-24}{8}) [/tex]
→
[tex] (\frac{6}{1}, \frac{-3}{1}) [/tex]
→
[tex] (6, -3) [/tex].
Thus the coordinates of B are:
[tex] \boxed{(6, -3)} [/tex]
