Midpoint coordinates of the given line segment
In this article we review calculating midpoint of the line segment with the given endpoints.
Segments $AB$ midpoint $C(x_m;y_m)$ coordinates, when segments endpoints are $A(x_1;y_1)$ and $B(x_2;y_2)$, can be calculated with these formulas: $${x_m=\frac{x_1+x_2}{2}, \ y_m=\frac{y_1+y_2}{2}}$$
Solved examples
Example No. 1
Find the midpoint $M$ coordinates of the line segment with the given endpoints $A(3,9)$ and $B(7,-5)$?
Using the formulas above, we get:
$$x_m=\frac{3+7}{2}=5, \ y_m=\frac{9+(-5)}{2}=2$$Answer: $M(x,y)=M(5,2)$
Example No. 2
Find the other endpoint $B$ coordinates of the line segment with the given endpoint $A(4,-12)$ and midpoint $M(8,11)$?
Using the formulas above, we get two equations and solve them:
$$8=\frac{4+x_2}{2}, \ x_2=12, \ 11=\frac{-12+y_2}{2}, \ y_2=34$$Answer: $B(x_2,y_2)=B(12,34)$
2019-02-26
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