What is the length of the median through vertex A of the triangle with vertices A(0, 0, 6), B(0, 4, 0), and C(6, 0, 0)?
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Question

What is the length of the median through vertex A of the triangle with vertices A(0, 0, 6), B(0, 4, 0), and C(6, 0, 0)?

Accepted Answer

The median from A meets BC at its midpoint D. The coordinates of D (midpoint of BC) are $\left(\frac{0+6}{2}, \frac{4+0}{2}, \frac{0+0}{2}\right) = (3, 2, 0)$. The length of median AD is the distance between A(0, 0, 6) and D(3, 2, 0), which is $\sqrt{(3-0)^2 + (2-0)^2 + (0-6)^2} = \sqrt{9 + 4 + 36} = \sqrt{49} = 7$.

Introduction to Three Dimensional Geometry

❓ Sibling Questions in this Chapter