How many diagonals can be constructed from one vertex of an n-gon? State your answer in terms of n and, of course, justify your
1 answer:
Answer:
Step-by-step explanation:
A diagonal is defined in geometry as a line connecting to two non adjacent vertices.
Therefore, the minimum number of sides a polygon must have in order to have a diagonal n - 3 sides as the 3 comes from the originating vertex and the other two adjacent vertices
Given that the polygon has n sides, the number of diagonals that can be drawn from each of those n sides gives the total number of diagonals as follows;
Total possible diagonals = n × (n - 3)
However, half of the diagonals drawn within the polygon are the same diagonals drawn in reverse. Therefore, the total number of distinct diagonals that can be drawn in a polygon is given as follows;
You might be interested in
Therefore, the equation of circle is:
- All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
- The radius of a circle is the separation between any point on the circle and its center.
- The radius must typically be a positive integer. Except when otherwise specified, this article discusses circles in Euclidean geometry, namely the Euclidean plane.
- A circle, specifically, is a straightforward closed curve that separates the plane into its inner and exterior.
Here we know thatbut we are not given the radius.
However, we can find the radius by using the distance formula.
, where
and
Putting the values, we get:
The radius comes out to be:
An equation of the circle with center and radius r is
Now, substituting the values, we get:
Therefore, the equation of circle is:
Know more about circles with the help of the given link:
#SPJ4