A certain polygon has its vertices at the following points. (2,4), (4,5), (6,4), and (4,3)
What is the best description of this polygon?
OA. pentagon
OB. rectangle
OC. square
OD. rhombus

Worth 30 points plz help quick I will report if you put anything

Step-by-step explanation:

When we plot the given vertices on a graph, We get a shape which has the following characteristics.

=> Opposite angles are equal.

=> The diagonals are perpendicular to each other.

=> Opposite sides are parallel to each other.

=> Sum of adjacent angles in equal to 90 degrees.

But, the shape does not seem to be like pentagon, square and rectangle. Hence, It's a rhombus.

See the attached file!

Hope this helped!

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.

step-by-step explanation:

milk=16 large

soda=280 kids

juice box=82 regular

63 soda +63 regular

124 large total