A fruit stand has to decide what to charge for their produce. They need $5 dollar for 1 apple and 1 orange. They also need $15 dollar for 3 apples and 3 oranges. Put this information into a system of linear equations. Can we find a unique price for an apple and an orange?

2

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3. parallelogram

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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.

where are the images of the functions i can only see the question you typed.

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it would take 7/10 of an hour too fill the pool.

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