Answer:
A. [tex] (-4, 5\frac{3}{5}) [/tex]
Step-by-step explanation:
Given:
A(-8, 6)
C(2, 5)
Required:
Coordinates of the point B that is ⅖ of AC
SOLUTION:
Solve using the formula below:
[tex] (x, y) = (x_1 + k(x_2 - x_1), y_1 + k(y_2 - y_1)) [/tex]
Let,
[tex] A(-8, 6) = (x_1, y_1) [/tex]
[tex] C(2, 5) = (x_2, y_2) [/tex]
[tex] k = \frac{2}{5} [/tex]
Thus, plug in the values as follows:
[tex] (x, y) = (-8 + \frac{2}{5}(2 -(-8)), 6 + \frac{2}{5}(5 - 6) [/tex]
[tex] (x, y) = (-8 + \frac{2}{5}(10), 6 + \frac{2}{5}(-1) [/tex]
[tex] (x, y) = (-8 + \frac{2*10}{5}, 6 + \frac{2*-1}{5}) [/tex]
[tex] (x, y) = (-8 + 4, 6 + (-\frac{2}{5})) [/tex]
[tex] (x, y) = (-4, 6 - \frac{2}{5}) [/tex]
[tex] (x, y) = (-4, \frac{30 - 2}{5}) [/tex]
[tex] (x, y) = (-4, \frac{28}{5}) [/tex]
[tex] (x, y) = (-4, 5\frac{3}{5}) [/tex]
