Question
Write the coordinates of the point dividing line segment joining points (2, 3) and (3, 4) internally in the ratio 1 : 5.
✓
Answer
Let the coordinates of the required point be (x, y), then
$\text{x}=\frac{\text{mx}_2+\text{mx}_1}{\text{m}+\text{n}}$ and $\text{y}=\frac{\text{my}_2+\text{my}_1}{\text{m}+\text{n}}$
Now, $\text{x}=\frac{1\times3+5\times2}{1+5}=\frac{3+10}{6}=\frac{13}{6}$
and $\text{y}=\frac{1\times4+5\times3}{1+5}=\frac{4+15}{6}=\frac{19}{6}$
Hence coordinates of the required point will be $\Big(\frac{13}{6},\frac{19}{6}\Big).$
$\text{x}=\frac{\text{mx}_2+\text{mx}_1}{\text{m}+\text{n}}$ and $\text{y}=\frac{\text{my}_2+\text{my}_1}{\text{m}+\text{n}}$
Now, $\text{x}=\frac{1\times3+5\times2}{1+5}=\frac{3+10}{6}=\frac{13}{6}$
and $\text{y}=\frac{1\times4+5\times3}{1+5}=\frac{4+15}{6}=\frac{19}{6}$
Hence coordinates of the required point will be $\Big(\frac{13}{6},\frac{19}{6}\Big).$
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