Ascientist recorded the movement of a pendulum for 10 s. the scientist began recording when the pendulum was at its resting position. the pendulum then moved right (positive displacement) and left (negative displacement) several times. the pendulum took 4 s to swing to the right and the left and then return to its resting position. the pendulum’s furthest distance to either side was 6 in. graph the function that represents the pendulum’s displacement as a function of time.

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.

hard

step-by-step explanation: