Question

3. Given the point A(-3,-2) and

B(6, 1), find the coordinates of the
point that partitions AB in the ratio
2:1.

Answer 1

The answers are (3,0) and (0,-1).

Explanation:

You get these answers by using the line partitioning formula:

P = x1 + k (x2 + x1)

Answer 2

let's say that point is point C.

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

`\bf C=\left(\cfrac{(1\cdot -3)+(2\cdot 6)}{2+1}\quad ,\quad \cfrac{(1\cdot -2)+(2\cdot 1)}{2+1}\right) \\\\\\ C=\left(\cfrac{-3+12}{3}~,~ \cfrac{-2+2}{3} \right)\implies C=\left( \cfrac{9}{3}~,~\cfrac{0}{3} \right)\implies C=(3~,~0)`