What are the coordinates of point $$B$$ on $$A C$$ such that the ratio of $$A B$$ to $$B C$$ is $$5:1$$ ? ![](http://admin.getprephub.com/media/editor/ag9_20230214202311737946.png)

Iet, $$B(x, y)$$ divides $$A C$$ in the ratio $$5: 1$$ $$A(-2,5)$$ and $$C(2,-5)$$ are the co-ordinates of $$A, C$$ respectively. By section formula,$$(\frac{m x_2+n x_1}{m+n}, \frac{m y+n y_1}{m + n})$$ Here, $$m=5, n=1, x_2=2, x_1=-2$$, or,$$y_2=-5$$ and $$y_1=5$$ Putting the value, $$(x, y) =(\frac{5 \cdot 2+1 \cdot(-2)}{5+1}, \frac{5 \cdot(-5)+2(5)}{5+1}) $$ $$=(\frac{10-2}{6}-\frac{25+5}{6}) $$ $$=(\frac{8}{6},-\frac{20}{6})=(\frac{4}{3},-\frac{10}{3})$$ $$ =(1 \frac{1}{3},-3 \frac{1}{3}) $$

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MCQ

What are the coordinates of point $B$ on $A C$ such that the ratio of $A B$ to $B C$ is $5:1$ ?

Select all that apply :

$(1 \frac{1}{3},-3 \frac{1}{3})$

$(1 \frac{1}{6},-3 \frac{1}{6})$

$(3 \frac{1}{6},-8 \frac{1}{6})$

$(3 \frac{1}{3},-8 \frac{1}{3})$

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