Answer:
[tex]B(x,y) = (-3,0)[/tex]
Step-by-step explanation:
Given
[tex]A = (6,-6)[/tex]
[tex]C = (-6,2)[/tex]
[tex]AB = \frac{3}{4} AC[/tex]
Required
Find coordinates of B
First, we need to convert [tex]AB = \frac{3}{4} AC[/tex] to ratio [tex]AB:BC[/tex]
SInce [tex]AB = \frac{3}{4} AC[/tex], then
[tex]AB : BC = 3 : 4 - 3[/tex]
[tex]AB : BC = 3 : 1[/tex]
The coordinates of B can then be calculated as follows;
[tex]B(x,y) = (\frac{nx_1 + mx_2}{n + m},\frac{ny_1 + my_2}{n + m})[/tex]
Where
[tex]A(x_1,y_1) = A(6,-6)[/tex]
[tex]C(x_2,y_2) = A(-6,2)[/tex]
[tex]m:n = 3 : 1[/tex]
Substitute these values in the given formula;
[tex]B(x,y) = (\frac{1 * 6 + 3 * -6}{1 + 3},\frac{1 * -6 + 3 * 2}{1 + 3})[/tex]
[tex]B(x,y) = (\frac{6 -18}{4},\frac{-6 + 6}{4})[/tex]
[tex]B(x,y) = (\frac{-12}{4},\frac{0}{4})[/tex]
[tex]B(x,y) = (-3,0)[/tex]
Hence, the coordinates of B is [tex](-3,0)[/tex]
