The distance between two points α and β is |α − β|.
The point that internally divides segment αβ in the ratio m:n is (nα + mβ)/(m+n).
Example ① Find the distance between α=1+i and β=4+5i.
Solution:|α−β|=|−3−4i|=5
Solution:|α−β|=|−3−4i|=5
Key Points
- Distance is the absolute value of the difference.
- The midpoint is (α+β)/2.
Practice Problems
- Find the midpoint of α=2+i and β=−1+3i.
Solution and Explanation
- Answer:1/2 + 2i