Question

Find the point, M, that divides segment AB into a ratio of 4:7 if A is at (-33, 0) and B is at (0, 44).

Answer 1

let's say the point is C, and divides AB on a 4:7 ratio, from A to B, meaning the AC segment takes 4 units of the lot and the CB segment takes 7.


`\bf ~~~~~~~~~~~~\textit{internal division of a line segment} \\\\\\ A(-33,0)\qquad B(0,44)\qquad \qquad \stackrel{\textit{ratio from A to B}}{4:7} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{4}{7}\implies \cfrac{A}{B} = \cfrac{4}{7}\implies 7A=4B\implies 7(-33,0)=4(0,44)\\\\ -------------------------------`


`\bf C=\left(\cfrac{\textit{sum of`