Answer:
[tex] (\frac{3}{13}, -3) [/tex]
Step-by-step explanation:
Apply the formula following formula to find the coordinate pair of the point that is 3/10 of the way from A(-3, -6) to B(11, 7):
[tex] x = \frac{mx_2 + nx_1}{m + n} [/tex]
[tex] y = \frac{my_2 + ny_1}{m + n} [/tex]
Where,
[tex] A(-3, -6) = (x_1, y_1) [/tex]
[tex] B(11, 7) = (x_2, y_2) [/tex]
[tex] m = 3, n = 10 [/tex]
Finding the x coordinate:
[tex] x = \frac{mx_2 + nx_1}{m + n} [/tex]
[tex] x = \frac{3(11) + 10(-3)}{3 + 10} [/tex]
[tex] x = \frac{33 - 30}{13} [/tex]
[tex] x = \frac{3}{13} [/tex]
[tex] y = \frac{my_2 + ny_1}{m + n} [/tex]
[tex] y = \frac{3(7) + 10(-6)}{3 + 10} [/tex]
[tex] y = \frac{21 - 60}{13} [/tex]
[tex] y = \frac{-39}{13} [/tex]
[tex] y = -3 [/tex]
The coordinates of the point 3/10 of the way from A to B are [tex] (\frac{3}{13}, -3) [/tex]
