11. * Quadrilateral ABCD has the following vertices: A(1, 4), B(6,4), C(1, -3), and D(-4, -3).
A dilation centered at the origin with a scale factor of 8 is applied to ABCD to form
A'B'C'D'. Which of the following statements is true?
O A) Quadrilateral ABCD and quadrilateral A'B'C'D' have the same area.
B) Quadrilateral ABCD and quadrilateral A'B'C'D' have the same perimeter.
C) Quadrilateral ABCD and quadrilateral A'B'C'D' have the same side lengths.
D) Quadrilateral ABCD and quadrilateral A'B'C'D' have the same angle measures.

D) Quadrilateral ABCD and quadrilateral A'B'C'D' have the same angle measures.

Step-by-step explanation:

A dilation basically just means that the shape gets proportionately larger (see attached file).

A cannot be true because of the dilation. The shape is now larger than it was by a factor of eight. Therefore the area will not be the same.

B and C are also not true for basically the same reasons. Shape is bigger, therefore the length of the sides are longer and the perimeter is larger.

The only thing that is not affected by a dilation are the shapes angle measures. If those were affected, A'B'C'D' would not be a dilation of ABCD.

Hope this helps.

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.