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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

1 (i) 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

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The line segment joining the points A (– 2, 3, 5) and B(1, – 4, 6)

Let point P(x,y,z) be the point that divides the line segment AB internally in the ratio 2:3.

Now, as we know by section formula, The coordinate of the point P, which divides line segment A(x_1,y_1,z_1) And B(x_2,y_2,z_2) in ratio m:n, 

\left (\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n},\frac{mz_2+nz_1}{m+n} \right )

Now the point that divides A (-2, 3, 5) and B (1, -4, 6) in ratio 2:3 is 

\left (\frac{2(1)+3(-2)}{2+3},\frac{2(-4)+3(3)}{2+3},\frac{2(6)+3(5)}{2+3} \right )=\left ( \frac{-4}{5},\frac{1}{5},\frac{27}{5} \right )

Hence, required point is: 

\left ( \frac{-4}{5},\frac{1}{5},\frac{27}{5} \right ). 

 

 

Posted by

Pankaj Sanodiya

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