First slide

Introduction to 3-D Geometry

Question

The point which divides the line segment joining $(- 3. - 2, 4)$ , $(- 1, - 4, 2)$ in the ratio $3 : 2$ internally is

Easy

A

$(- 3, 8, - 2)$
B

$(3, - 8, - 2)$
C

$(3, 2, 4)$
D

$(- \frac{9}{5}, - \frac{16}{5}, \frac{14}{5})$

Solution

The point which divides the line segment joining the points $A (x_{1}, y_{1}, z_{1})$ and $B (x_{2}, y_{2}, z_{2})$ in the ratio $m : n$ internally is $P (\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n}, \frac{m z_{2} + n z_{1}}{m + n})$
The point which divides the line segment joining $(- 3. - 2, 4)$ , $(- 1, - 4, 2)$ in the ratio $3 : 2$ internally is $P (- \frac{9}{5}, - \frac{16}{5}, \frac{14}{5})$

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