# If the point R is the mid-point of the line joining the points C(5, 1, 3) and D(- 1, 1, -1) then find the point R ?

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If the point R is the mid-point of the line joining the points C(5, 1, 3) and D(- 1, 1, -1) then find the point R ?
1. (2, 1, - 1)
2. (2, 3, 1)
3. (1, 1, 1)
4. (2, 1, 1)

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Correct Answer - Option 4 : (2, 1, 1)

Concept:

Let A(x1, y1, z1) and B(x2, y2, z2) be two points on a 3D plane then mid-point of the line joining the points A and B is given by: $\rm (\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}, \frac{z_{1}+z_{2}}{2}).$

Calculation:

Given: R is the mid-point of the line joining the points C(5, 1, 3) and D(- 1, 1, -1).

As we know that, the mid-point of the line joining the points A(x1, y1, z1) and B(x2, y2, z2) is given by: $\rm (\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}, \frac{z_{1}+z_{2}}{2}).$

$\Rightarrow \rm R=(\frac{5-1}{2}, \frac{1+1}{2} ,\frac{3-1}{2} )=(2, 1, 1)$

Hence, the correct option is 4.

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