Campsite f and g are on opposite sides of the lake a survey crew made measurements on the diagram. What is the distance between the 2 campsites

GF is 42.3 meters

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Verify if segment AB is parallel to segment FG

we know that

If segment AB is parallel to segment FG

then

Triangle ABO would be similar to Triangle GFO by AA Similarity theorem

Remember that

If two figures are similar, then the ratio of its corresponding sides is proportional

so

substitute the given values

Multiply in cross

Is true

Therefore

Corresponding sides are proportional

segment AB is parallel to segment FG

Triangle ABO is similar to Triangle GFO by AA Similarity theorem

Find the distance between the two campsites FG

Applying proportion

substitute

solve for GF

123

step-by-step explanation:

agngel

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!