Fredric leads a team of hikers for a full-day hike. the total elevation gain during the hike is 2,100 feet. all of the hikers have to pass two checkpoints before they reach the peak. the elevation gain from the starting point to checkpoint 1 is 100 feet less than double the elevation gain from checkpoint 2 to the peak. the elevation gain from checkpoint 1 to checkpoint 2 is the mean of the elevation gain from the start to checkpoint 1 and the elevation gain from checkpoint 2 to the peak. let x represent the elevation gain from the starting point to checkpoint 1, y represent the elevation gain from checkpoint 1 to checkpoint 2, and z represent the elevation gain from checkpoint 2 to the peak. which augmented matrices represent the context of this scenario?

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!

answer: i think it's a

step-by-step explanation: