Question

Find the point, M, that divides segment AB into a ratio of 5:6 if A is at (0, 22) and B is at (11, 0). A) (5, 12) B) (5, 11) C) (6, 12) D) (6, 11)

Answer 1

$\bf \left. \qquad \right.\textit{internal division of a line segment} \\\\\\ A(0,22)\qquad B(11,0)\qquad \qquad 5:6\quad \textit{from A to B} \\\\\\ \cfrac{AM}{MB} = \cfrac{5}{6}\implies \cfrac{A}{B} = \cfrac{5}{6}\implies 6A=5B\implies 6(0,22)=5(11,0)\\\\ -------------------------------$

$\bf { M=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)}\\\\ -------------------------------\\\\ M=\left(\cfrac{(6\cdot 0)+(5\cdot 11)}{5+6}\quad ,\quad \cfrac{(6\cdot 22)+(5\cdot 0)}{5+6}\right) \\\\\\ M=\left( \cfrac{55}{11}~~,~~\cfrac{132}{11} \right)$

and surely you know what that is.

Answer 2

Answer:

Answer is (5,12) if anyone wanted to know

Step-by-step explanation: