Triangle Vertices Calculator

Find Triangle Vertices from Midpoints

If $D$, $E$, and $F$ are midpoints of sides $BC$, $AC$, and $AB$, the vertices are:

$$A = (x_1 + x_3 - x_2,\; y_1 + y_3 - y_2)$$

$$B = (x_1 + x_2 - x_3,\; y_1 + y_2 - y_3)$$

$$C = (x_2 + x_3 - x_1,\; y_2 + y_3 - y_1)$$

Midpoints $D(2,3)$, $E(4,3)$, $F(3,1)$ give vertices $A(1,1)$, $B(3,5)$, and $C(5,1)$.

How many vertices does a triangle have?

Three. Each vertex is where two sides meet.

Can I find vertices from just one midpoint?

No. You need all three midpoints to uniquely determine the triangle vertices.

What is the midpoint formula?

The midpoint of segment from $(x_a, y_a)$ to $(x_b, y_b)$ is $((x_a+x_b)/2,\; (y_a+y_b)/2)$.

Do the midpoint formulas work in 3D?

Yes. Add or subtract the z-coordinates the same way as x and y.