Study guide and
3 practice problems
on:
Midpoint between two vectors
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The midpoint between the two vectors $\mathbf{x}$ and $\mathbf{y}$ is $\frac{\mathbf{x} + \mathbf{y}}{2}$.
Related topics
Vectors
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Multivariable calculus
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Geometric proofs with vectors
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Practice problems
Consider an arbitrary quadrilateral. The two blue line segments connect the midpoints of adjacent sides. Using only vector addition and multiplication by constants, show that these line segments are parallel and have the same length.
Solution
Show that the line connecting the midpoints of two sides of a triangle is parallel to and half the length of the third side.
Solution
Use vector addition, subtraction, and scalar multiplication to show that the midpoint between the two points $\mathbf{x}$ and $\mathbf{y}$ is $\frac{\mathbf{x} + \mathbf{y}}{2}$.
Solution