Answer:
R(1.6, 0)
Step-by-step explanation:
Use the formula, [tex] (x, y) = (x_1 + k(x_2 - x_1), y_1 + k(y_2 - y_1)) [/tex] to find the coordinates of point R, that partition the lie segment AB into the ratio 1/5.
Let,
[tex] A(1, -1) = (x_1, y_1) [/tex]
[tex] B(4, 4) = (x_2, y_2) [/tex]
Thus, plug in the values as follows:
[tex] R(x, y) = (1 + \frac{1}{5}(4 - 1), -1 + \frac{1}{5}(4 -(-1)) [/tex]
[tex] R(x, y) = (1 + \frac{1}{5}(3), -1 + \frac{1}{5}(4 + 1) [/tex]
[tex] R(x, y) = (1 + \frac{1}{5}(3), -1 + \frac{1}{5}(5) [/tex]
[tex] R(x, y) = (1 + \frac{3}{5}, -1 + \frac{5}{5}) [/tex]
[tex] R(x, y) = (\frac{5 + 3}{5}, -1 + 1) [/tex]
[tex] R(x, y) = (\frac{8}{5}, 0) [/tex]
[tex] R(x, y) = (1.6, 0) [/tex]
The coordinates of point R, are (1.6, 0)
