Answer to Question #130909 in Analytic Geometry for balbina

Question

find the midpoint
(-2 7/8, 5/8), (-3 1/4, 1/2)

Answer 1

How do you find a number halfway between two numbers? You take their average. For instance, what's halfway between $10$ and $20$? It's $\frac{10+20}2=15$.

You can use the same argument for two points. Since we need to find the midpoint of two 2D points, just take the average of their corresponding x and y coordinates.

Thus, x coordinate of the midpoint

$$=\frac{(-2 \frac78)+(-3 \frac14)}2=\frac{(-\frac{23}8)+(-\frac{13}4)}2=-\frac{49}{16}$$

y coordinate of the midpoint

$$=\frac{\frac58+\frac12}2=\frac{9}{16}$$

Thus, the midpoint of the two points is $\left(-\frac{49}{16},\frac9{16}\right)$.