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P-2 Co-ordinate Geometry — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsP-2 Co-ordinate Geometry3 Marks
Question
If point $\mathrm{P}(-4,6)$ divides the line segment $\mathrm{AB}$ with $\mathrm{A}(-6,10)$ and $\mathrm{B}(\mathrm{r}, \mathrm{s})$ in the ratio $2: 1$, find the co-ordinates of $B$.
✓

Answer

By section formula
$-4=\frac{2 \times r+1 \times(-6)}{2+1}$
$6=\frac{2 \times s+1 \times 10}{2+1}$
$\therefore-4=\frac{2 r-6}{3}$
$\therefore 6=\frac{2 s+10}{3}$
$\therefore-12=2 r-6$
$\therefore 18=2 \mathrm{~s}+10$
$\therefore 2 \mathrm{r}=-6$
$\therefore 2 \mathrm{~s}=8$
$\therefore \quad r=-3$
$\therefore \mathrm{s}=4$
$\therefore$ co-ordinates of point $\mathrm{B}$ are $(-3,4)$.

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