Points R and S on the coordinate grid below show the positions of two midfield players of a soccer team:
Coordinate grid shown from negative 4 to positive 4 on x-axis and negative 4 to positive 4 on y-axis. From the origin, point R is 1 unit to the left and 3.5 units down. From the origin, point S is 1 unit to the left and 3.5 units up.
Which statement best describes the relationship between the positions of the two midfield players?

A. S is R reflected across the y-axis; only the signs of the x-coordinates of R and S are different.
B. S is R reflected across the y-axis; only the signs of the y-coordinates of R and S are different.
C. S is R reflected across the x-axis; only the signs of the x-coordinates of R and S are different.
D. S is R reflected across the x-axis; only the signs of the y-coordinates of R and S are different.

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

i did it myself and i got 4.2 (b) hope its right

step-by-step explanation:

i dont know men

step-by-step explanation: