Use the Distance Forumla to find the lengths of the diagonals of a polygon with vertices A(0.3), B(3,3), C(4,1), D(0,-1), and E(-2,1). Please explain this =)
1. Draw a sketch of the polygon: It is an irregular convex pentagon.
2. A pentagon has 5 diagonals. The length of two of the 5 diagonals is obvious:
|AD| = 4 and |CE| = 6
3. The distance between the points $\displaystyle P_1(x_1\ ,\ y_1)$ and $\displaystyle P_2(x_2\ ,\ y_2)$ is calculated by:
$\displaystyle d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$
4. The length of AC:
$\displaystyle d(AC) = \sqrt{(0 - 4)^2 + (3 - 1)^2} = \sqrt{16+4}=\sqrt{20}=2\sqrt{5}$
5. The last two diagonals are calculated in just the same way. Good luck!