Simple Math?

Question

1.Find the perpendicular bisector of the segment joining the points A(7,3) and B(-1,4)
2. How many diagonals are there in a 10 sided polygons?
*** easy way to get a best answer, correct answer and explanation. come on, you can do it.

Answer 1

1. Find the midpoint, then the negative slope, that will give you an equation for a line that is a bisector.

The midpoint is halfway between A and B. The midpoint is the average of the x-coords and the average of the y-coords.

x(mid) = [ x(A) - x(B) ] / 2
x(mid) = [ 7 - (-1) ] / 2
x(mid) = 8 / 2
x(mid) = 4

y(mid) = [ y(A) - y(B) ] / 2
y(mid) = [ 3 - 4 ] / 2
y(mid) = -1 / 2
y(mid) = -1/2

So your midpoint is (4, -1/2)

Now the slope of the line AB is given by the formula (y2 - y1) / (x2 - x1).

m = (4-3) / (7 -(-1) )
m = 1 / 8
m = 1/8

That means the perpendicular line must have a slope equal to the negative reciprocal:

m' = -1/m
m' = -1/(1/8)
m' = -8

So you have a point (4, -1/2) and a slope (-8).

Using the point slope form, you can get an equation of the line:
y - y(mid) = slope (x - x(mid))
y - (-1/2) = (-8)(x - 4)
y + 1/2 = -8x + 32
y = -8x + 31.5

2. For each vertex, you can connect to (n-3) other vertices. For example with ten vertices, you can connect to 7 other vertices. This excludes the point itself and the two adjacent vertices that would make up the outside of the polygon.

Since there are 10 vertices and 7 ways for each to connect that would be 70 connections. But connecting A to B is the same as connecting B to A, so we have actually counted everything twice. Therefore divide by 2 to get 70/2 = 35 diagonals.

In general, for an n-sided polygon there are n(n-3)/2 diagonals. For n = 10, there are 35 diagonals.

Answer 2

= 7/3 pi