Commute Home
Mrs. Washington lives 20 miles from
her office and drives her car to and
from work every day. The graph below
shows her distance from home over
time as she drove home from work
one day.
Distance from Home (miles)
2
4 6
8 10 12 14 16 18 20 22 24 26 28 30 32 34
Time (minutes)
Answer the following questions about the problem above. Write in complete sentences to get full credit.
1. What is the slope for section "b" of Mrs. Washington's commute.
2. What is the slope for section "C" of Mrs Washington's commute?
3. Explain the difference in "b" and "c" in context of Mrs. Washing driving home.
4. How far does Mrs. Washington live from her work?

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!

a negative exponent is translated as follows:

so, we have

add 5 subtract 1

step-by-step explanation: