A cartographer creates a map of Bucks County with a scale factor of 1 inch = 10 miles. The distance between Quakertown and Sellerville is 2.92 inches on the map. Determine the actual distance between the two boroughs.

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.

using pemdas, (order of operations) you'll see the answer is 24.

150

step-by-step explanation:

(sorry i'm not typing it again just read the other two explanation sections i just typed it'll be the same.)