Question

What is the perimeter of a polygon with vertices at (-6,-1) (-3,-4) (6,5) and (3,8) ​?

Answer 1

The formula of the distance between 2 points states that the distance AB between points A(a, b) and B(c, d) is found as follows:


`\displaystyle{ AB= √((a-c)^2+(b-d)^2)`.


Let the points of the polygon be A(-6,-1), B(-3,-4), C(6,5) and D(3,8). Then, the perimeter of the polygon ABCD is

AB+BC+CD+DA.

We can find each of AB, BC, CD, DA by the Distance Formula as follows:



`\displaystyle{ AB= √((-6+3)^2+(-1+4)^2)=√(9+9)=√(2\cdot9)=3√(2)`.


`\displaystyle{ AB= √((6+3)^2+(5+4)^2)=√(81+81)=√(2\cdot81)=9√(2)`.


`\displaystyle{ AB= √((6-3)^2+(5-8)^2)=√(9+9)=3√(2)`.


`\displaystyle{ AB= √((-6-3)^2+(-1-8)^2)=√(81+81)=9√(2)`.


Thus, the perimeter of the polygon is


`9√(2)+9√(2)+3√(2)+3√(2)=24√(2)` (units).


Answer:
`24√(2)` units