Quadrilateral MNOP is dilated by a scale factor of ; to form quadrilateral M'N'O'P'. What is the measure of side P'M'?

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.

the answer is a i belaeve atleast thats what my calculator just gfave me

step-by-step explanation:

1) 2/5

2) zero=0/1

3) zero=0/2

4) -4/5

5) undefined=3/0

i'm sorry mate, but i am not seeing any figures. i am unable to solve this for you.