The side lengths of a rectangular figure are dilated by a scale factor of 1/3. Which statement describes the figure that results? 1. The area of the original figure is 9 times the area of the figure that results.

2. The perimeter of the original figure is 9 times the perimeter of the figure that results.

3. The area of the original figure is 6 times the area of the figure that results.

4. The perimeter of the original figure is 6 times the perimeter of the figure that results.

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.

you should at least use a calculater

step-by-step explanation:

answer: d. $20

step-by-step explanation:

just took the test

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