Geometry HELP ME

Question

A city planner designs a park that is a quadrilateral with vertices at J(-3, 1), K(3, 3), L (5, -1), and

M (-3, -1). There is an entrance to the park at the midpoint of each side of the park. A straight path

connects each entrance to the entrance on the opposite side. Assuming each unit of the coordinate

plane represents 10 meters, what is the total length of the paths to the nearest meter? Round your

answer to the nearest whole number. The total length of the paths is approximately _ meters?

Answer 1

midpoints have coordinates which are the average of the endpoints' coordinates

= (-3, -1) to (5,-1) have midpoint ((5-3)/2, -1) = (1,-1)

opposite side has midpoint of (-3,1) and (3,3) = (0,2)

midpoints are (1,-1) and (0,2) with distance of sqr(1^2 +3^2)

=sqr(10) converts to 3.162(10) = about 31.62 meters

and the other two sides' midpoints:

=(-3,0) to (4,,1) with distance of sqr(7^2 +1^2)

=sqr(50) converts to about 7.071(10) = about 70.71 meters

total length of the paths = [sqr(10) + sqr(50)]10 = 102.33 meters = about 102 meters

= sqr(10)[1+sqr(5)]= about 3.16(3.24)=about 10.2, convert to meters, multiply 10 = 102 meters