By definition, a quadrilateral is a two-dimensional figure that is composed of four sides. Since you are given with the coordinates of the vertices, the first logical thing to do is to plot the points in a Cartesian plane as shown in the attached picture. Next, find the midpoints of each side of the quadrilateral as denoted by the red dots. Then, create a line connecting the opposite midpoints which represents the length of the paths.
Our first solution is to find the midpoint of each sides. This is done by taking the average of each coordinate. The equation would be:
x,midpoint = (x₁+x₂)/2
y,midpoint = (y₁+y₂)/2
So, applying the equation:
midpoint jk = (-3+1/2, 1+3/2) = (-1,2)
midpoint kl = (1+5/2, 3+⁻1/2) = (3,1)
midpoint ml = (5+⁻1/2, ⁻1+⁻3/2) = (2,-2)
midpoint jm = (⁻3+⁻1/2, 1+⁻3/2) = (-2,-1)
Next, we find the lengths of the paths by using the distance formula:
d = √(x₂ - x₁)² + (y₂ - y₁)²
Distance between jk and ml = √(⁻1-2)² + (2 - ⁻2)² = 5
Distance between jm and kl = √(3-⁻2)² + (1-⁻1)² = √29
Total distance = 5 + √29 = 10.385 units
Since the scale is 1 unit = 10 meters, the actual total length of paths is equal to:
Actual Total Distance = 10.385*10
Actual Total Distance = 103.85 meters
