Agroup of 10 friends decides to head up to a cabin in the woods (where nothing could possibly go wrong). unfortunately, a number of these friends have dated each other in the past, and things are still a little awkward. to 4.3. coloring 224 get the cabin, they need to divide up into some number of cars, and no two people who dated should be in the same car. (a) what is the smallest number of cars you need if all the relationships were strictly heterosexual

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.