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External Division

The coordinat...

Question

The coordinates of the mid-point of the line segment joining two points P(X₁, y₁, z₁) and Q(x₂, y₂, z₂) are:

A

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B

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C

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D

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Solution

The correct option is D

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Similar questions

The distance between the points P(x₁, y₁, z₁) and Q (x₂, y₂, z₂) is given by:

x_{1}, x_{2}, y_{1}, y_{2} ϵ R

x_{1}

x_{2}, y_{1} = y_{2}

z_{1} = x_{1} + i y_{1}, z_{2} = x_{2} + i y_{2}

z_{3} = \frac{1}{2} (z_{1} + z_{2})

z_{1}, z_{2}, z_{3}

For the line segment joining the points A(x1, y₁, z₁) and B(x₂, y₂, z₂)

are

x_{1} = 3 y_{1} + 2 y_{2} - y_{3}, y_{1} = z_{1} - z_{2} + z_{3} x_{2} = - y_{1} + 4 y_{2} + 5 y_{3}, y_{2} = z_{2} + 3 z_{3} x_{3} = y_{1} - y_{2} + 3 y_{3}, y_{3} = 2 z_{1} + z_{2}

x_{1},

z_{1}, z_{2}, z_{3}

x_{1} = z_{1} - 2 z_{2} + k z_{3}

, what is the value of k?

Show that the coordinates of the centroid of the triangle with vertices $A (x_{1}, y_{1}, z_{1})$ , $B (x_{2}, y_{2}, z_{2})$ and $C (x_{3}, y_{3}, z_{3})$ is $(\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3}, \frac{z_{1} + z_{2} + z_{3}}{3})$ .

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External Division

Standard XII Mathematics