Question

Point P partitions directed segment AB in the ratio of 4:4.

If A(4,-1) and B(1,3), find the y-coordinates of P.

Answer 1

you know, we could use the ratio method to get it using ratios, but the ratio is 4:4, or namely 1:1, which means the point P is the midpoint of AB, in which case, we can simply use the Midpoint formula to get P.

`~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{4}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 1 + 4}{2}~~~ ,~~~ \cfrac{ 3 -1}{2} \right)\implies \left( \cfrac{5}{2}~~,~~1 \right)`