Question

Line segment AB has endpoints A(1, 4) and B(6, 2). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 2:3.

Answer 1

D. ( 24/5, 19/5)

Explanation:

(mx2 + nx1) (my2 + ny1)

(m + n) , (m + n)

Where the point divides the segment internally in the ratio m:n

((2)(3) + (3)(6)) ((2)(8) + (3)(1))

(2 + 3) , (2 + 3) = 24/5, 19/5

Answer 2

let's say that point is point C, thus

`\bf ~~~~~~~~~~~~\textit{internal division of a line segment}\\\\\\A(1,4)\qquad B(6,2)\qquad\qquad \stackrel{\textit{ratio from A to B}}{2:3}\\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{2}{3}\implies \cfrac{A}{B} = \cfrac{2}{3}\implies 3A=2B\implies 3(1,4)=2(6,2)\\\\[-0.35em]~\dotfill\\\\C=\left(\frac{\textit{sum of`

`\bf C=\left(\cfrac{(3\cdot 1)+(2\cdot 6)}{2+3}\quad ,\quad \cfrac{(3\cdot 4)+(2\cdot 2)}{2+3}\right)\implies C=\left(\cfrac{3+12}{5}~,~\cfrac{12+4}{5} \right)\\\\\\C=\left( \cfrac{15}{5}~,~\cfrac{16}{5} \right)\implies C=\left( 3~,~3(1)/(5) \right)`