The vertices of a quadrilateral in the coordinate plane are known. how can the perimeter of the figure be found?

Find the length of sides. The sum of these sides is the perimeter of a quadrilateral

Step-by-step explanation:

A quadrilateral is a figure that has four sides. To find the perimeter of any quadrilateral, we find the sum of all four sides.

Given:

The co-ordinates of all vertices of a quadrilateral is known

To Find:

Perimeter of a quadrilateral

Steps:

1. Find the length of all sides using the straight line distance formula.

2. Add all the sides to find perimeter.

Let us take an example:

In figure the four co-ordinates are as follows:

A(1,3), B(4,2), C(3,0) and D(1,1)

Perimeter of quadrilateral ABCD= AB+BC+CD+DA

To find AB we use straight line distance formula, which is as follows:

AB = where

Substituting values we get,

AB=

AB=

AB=

AB=

Similarly, we can find length of BC,CD and DA

BC= ,CD= ,DA=2

Then sum of these sides is perimeter of quadrilateral=

Note: In this example, the perimeter cam out in roots, due to the values of co-ordinates taken. But the sum can also be a whole number.

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i