# ABCDEFGH is a regular convex octagon, with #A( 0, 1 ), B( sqrt2, 1 ), E( sqrt 2, -1-sqrt 2 ) and F( 0, -1-sqrt2 )#. How do you find the coordinates of the remaining vertices? .

##### 2 Answers

Not so sure, but here is what I think one would do if they had solve this problem (or a similar one with different points).

Average all x values and y values

So the center point is

Translate the center point to zero (change all x values by

Then, rotate each point by 90 degrees. (

Finally, translate each of these new points back to their original positions. (increase all x values by

Depending on how the octagon was set up,

A' = G, B'=H, F'=D, E'=C

#### Explanation:

As AB is in y-direction, side of the octagon L =

From the averages of the coordinates of A, B, E and F, the center M

has coordinates

#(x_M, y_M)=(1/sqrt2, -1/sqrt2).

C, D, G and H are equidistant from M. in the directions of the x and y

axes. These have the common distances

d_x = (side of octagon)

From symmetry, the remaining vertices are