SOLUTION: A regular hexagon of side length 2a is placed so that the center is at the origin, and one diagonal lies on the y-axis. Find the coordinate of the vertex located in Quadrant III.

Question 1025522: A regular hexagon of side length 2a is placed so that the center is at the origin, and one diagonal lies on the y-axis. Find the coordinate of the vertex located in Quadrant III.
Note: if drawn properly, the regular hexagon should only have one point IN Quadrant III. Your answer must be in terms of a.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A regular hexagon of side length 2a is placed so that the center is at the origin, and one diagonal lies on the y-axis. Find the coordinate of the vertex located in Quadrant III.
----------------
The side length of a hexagon = radius
The angle of that vertex = 60 + 60 + 60 + 30 = 210 degs
-----
x = 2a*cos(210) = -sqrt(3)a
y = 2a*sin(210) = -a
---
--> (-sqrt(3)a,-a)
RELATED QUESTIONS
Find the equation of a circle whose radius is 5 and the center lies on the positive side... (answered by ikleyn,MathTherapy)

A rectangular box is to be placed in the first quadrant in such a way that one side lies... (answered by MathLover1)

Overlay a rectangular coordinate system on a Little League baseball diamond so that the... (answered by textot)

The area of a particular regular hexagon is x^3 square units, where x is the measure of... (answered by Earlsdon)

Length of major axis=4 Length of minor axis=2 Foci on y-axis. Center at the... (answered by Edwin McCravy)

a regular hexagon has aperimeter of 90cm find the length of one side of the... (answered by Cromlix)

Each edge and diagonal of a regular hexagon (15 in total) is colored red or black such... (answered by greenestamps)

A satellite dish is shaped like a paraboloid of revolution. This means that it can be... (answered by onyulee)

the center of a circle lies on the line x + y = 1 and passes through the origin and the... (answered by nyc_function)