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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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