Maths · Coordinates of a point in space, the distance between two points, section formula
If and are co-ordinates of the points of trisection of the segment joining the p
If \( z_{1} \) and \( z_{2} \) are \( z \) co-ordinates of the points of trisection of the segment joining the points \( \boldsymbol{A}(\mathbf{2}, \mathbf{1}, \mathbf{4}), \boldsymbol{B}(-\mathbf{1}, \mathbf{3}, \mathbf{6}) \) then \( z_{1}+z_{2}= \)
- A. 1
- B. 4
- C. 5 \)
- D. 10
Step-by-step solution
The points of trisection divide AB in ratios 1:2 and 2:1. Using section formula for z-coordinate: first point: (1*6+2*4)/3 = 14/3; second point: (2*6+1*4)/3 = 16/3. Sum = 30/3 = 10.
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