What is the number of diagonals that intersect at a given vertex of a hexagon, heptagon, 30-gon and n-gon?

i. 9

ii. 14

iii. 405

iv.

Step-by-step explanation:

The number of diagonals in a polygon of n sides can be determined by:

where n is the number of its sides.

i. For a hexagon which has 6 sides,

number of diagonals =

                                   =

                                   = 9

The number of diagonals in a hexagon is 9.

ii. For a heptagon which has 7 sides,

number of diagonals =

                                   =

                                   = 14

The number of diagonals in a heptagon is 14.

iii. For a 30-gon;

number of diagonals =

                                          =

                                         = 405

The number of diagonals in a 30-gon is 405.

iv. For a n-gon,

number of diagonals =

The number of diagonals in a n-gon is

answer: -8.2562234e+13

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.