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# Find the coordinates of the point which divides the line segment joining the points $(-2,3,5)$ and $(1,-4,6)$ in the ratio $2:3$ internally.

$\begin{array}{1 1}\big(-\large\frac{4}{5},\frac{1}{5},\frac{27}{5}\big) \\(-8,17,3) \\ \big(\large\frac{8}{5},\frac{17}{5},\frac{27}{5}\big) \\ \big(-\large\frac{8}{5},\frac{1}{5},\frac{27}{5}\big)\end{array}$

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## 1 Answer

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Toolbox:
• Section formula: The coordinates of the point $C$ that divides the segment joining the points $A(x_1,y_1,z_1)$ and $B(x_2,y_2,z_2)$ in the ratio $l:m$ internally is given by $C\big(\large\frac{lx_2+mx_1}{l+m},\frac{ly_2+my_1}{l+m},\frac{lz_2+mz_1}{l+m}\big)$
Given two points are $A(-2,3,5)$ and $B(1,-4,6)$
We know that from section formula the coordinates of the point $C$ that divides
the segment joining the points $A(x_1,y_1,z_1)$ and $B(x_2,y_2,z_2)$ in the ratio $l:m$ internally is given by
$C\big(\large\frac{lx_2+mx_1}{l+m},\frac{ly_2+my_1}{l+m},\frac{lz_2+mz_1}{l+m}\big)$
$\therefore$ the coordinates of the point $C$ which divides $AB$ in the ratio $2:3$ internally is
$C\big(\large\frac{2.1+3.(-2)}{2+3},\frac{2.(-4)+3.3}{2+3},\frac{2.6+3.5}{2+3}\big)$
$=C\big(-\large\frac{4}{5},\frac{1}{5},\frac{27}{5}\big)$
answered May 5, 2014

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