Point A is located at (5, 10) and point B is located at (20, 25).What point partitions the directed line segment AB into a 3:7 ratio?(9 1/2, 14 1/2)(9 1/2, 20 1/2)​(15 1/2, 14 1/2)​​(15 1/2, 20 1/2)​

Answer:[tex](9\frac{1}{2}, 14\frac{1}{2})[/tex]Step-by-step explanation:The given points are [tex]A(5,10)[/tex] and [tex]B(20,25)[/tex].We want to find the coordinates of the point that partitions the directed line segment AB into a 3:7 ratio.The point that partitions a directed line segment into a [tex]m:n[/tex] ratio is given by the formula;[tex](\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n})[/tex]
We substitute the given points and evaluate to obtain;
[tex](\frac{3(20)+7(5)}{3+7}, \frac{3(25)+7(10)}{3+7})[/tex]
[tex]\Rightarrow (\frac{60+35}{10}, \frac{75+70}{10})[/tex]
[tex]\Rightarrow (\frac{95}{10}, \frac{145}{10})[/tex]
[tex]\Rightarrow (9\frac{1}{2}, 14\frac{1}{2})[/tex]
The correct answer is A.