Each card in a deck has a positive integer written on one side. bjorn and dagmar each draw two cards and divide the number on the first card by the number on the second card to calculate their score. did bjorn get a higher score than dagmar?
(1) if bjorn had drawn the same two cards in the opposite order, his score would have been lower than dagmar’s score.
(2) the first card dagmar drew had a greater number than her second card.

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.

multiple all that

step-by-step explanation:

27×17