Consider the graph of quadrilateral ABCD, what is the most specific name for quadrilateral ABCD ?

The missing figure is attached down

The most specific name for  quadrilateral ABCD is parallelogram

Step-by-step explanation:

The quadrilateral is a parallelogram if

From the attached figure

∵ The diagonals of the quadrilateral are AC and BD

∵ A = (-2 , 3) , C = (0 , -3)

- Find the slope of AC and its length using the rule of the slope

   and the rule of the distance

∵

∴

∵

∴

- Find the mid-point of AC

∵

∴

∵ B = (2 , 2) , C = (-4 , -2)

- Find the slope of AC and its length using the rule of the slope

   and the rule of the distance

∵

∴

∵

∴

- Find the mid-point of AC

∵

∴

∵ ⇒ diagonals bisect each other

∵ ≠ ⇒ diagonals not equal in length

∵ The product of their slopes = -3 × = -2

∵ The product of the slopes of the perpendicular lines is -1

∴ AC and BD are not perpendicular

∴ ABCD is a parallelogram

The most specific name for  quadrilateral ABCD is parallelogram

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step-by-step explanation:

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step-by-step explanation:

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