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Question

# Use the points A(-1,2,4),B(0,6,-3), and C(2,-4,1). Write parametric equations for the line through C and the midpoint of AB.

Solution

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The midpoint $M$ of the line segment $PQ$ with endpoints $P(x_1,y_1,z_1)$ and $Q(x_2,y_2,z_2)$ in the Cartesian space is given by:

$M=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2},\dfrac{z_1+z_2}{2}\right)$

First, we let $M$ be the midpoint of $AB$ which is:

$M=\left(\dfrac{-1+0}{2},\dfrac{2+6}{2},\dfrac{4+(-3)}{2}\right)= \left(-\dfrac{1}{2},4,\dfrac{1}{2}\right)$

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