❗️5 points❗️
4. State the slope of the line.
A. 1
B. 0
C. undefined
D. -4

C. undefined.

Step-by-step explanation:

Find the slope of the line, using the following equation:

m = (y₂ - y₁)/(x₂ - x₁)

Find two points that are located on the line.

Let:

(x₁ , y₁) = (-4 , 0)

(x₂ , y₂) = (-4 , 1)

Plug in the corresponding numbers into the corresponding variables.

m = (1 - 0)/(-4 - (-4))

Note that when you have two negative signs directly next to each other, it becomes an addition:

m = (1)/(-4 + 4) = 1/0

You cannot have a slope of rise 1, run 0, so your answer is undefined.

C. undefined.

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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.

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