Answer:
(9, 2)
Step-by-step explanation:
What point divides the directed line segment AB¯¯¯¯¯ into a 3:1 ratio?
coordinate plane with segment A B with A at (0, 2) and B at (12, 2)
(3, 2)
(4, 2)
(8, 2)
(9, 2)
Solution:
If point O(x, y) divides the line segment AB with endpoints A([tex]x_1,y_1[/tex]) and B([tex]x_2,y_2[/tex]) in the ratio n:m, 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]
Let us assume C(x, y) is the point that divides segment A B with A at (0, 2) and B at (12, 2) in the ratio 3 : 1. Hence:
[tex]x=\frac{3}{3+1}(12-0)+0=\frac{3}{4}(12)=9 \\\\y=\frac{3}{3+1}(2-2)+2=\frac{3}{4}(0)+2=2[/tex]
Therefore the coordinate of point C is at (9, 2).
