Answer:
B(-3, -3)
Step-by-step explanation:
If a point O(x, y) divides line segment XY in the ratio of n:m and the endpoints of the segment are [tex]X(x_1,y_1)\ and\ Y(x_2,y_2)[/tex], the coordinates of O is:
[tex]x=\frac{n}{n+m}(x_2-x_1)+x_1 \\\\y=\frac{n}{n+m}(y_2-y_1)+y_1[/tex]
Given that A(6, -6) and C(-6, 2). Pont B is on AC such that:
AB = (3/4)AC
AB/AC = 3/4
Therefore point B divides the line AC in the ratio of 3:1. Let point B be at (x, y), therefore:
[tex]x=\frac{3}{3+1}(-6-6)+6=\frac{3}{4}(-12)+6=-9+6=-3\\ \\y=x=\frac{3}{3+1}(-2-(-6))-6=\frac{3}{4}(4)-6=3-6=-3[/tex]
Therefore the location of B is at (-3, -3)
