chaudhrym8275
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mhanifa

Answer:

  • Rhombus

Step-by-step explanation:

Refer to attached

You can easily calculate that each of the sides have the length:

  • AB= BC = CD = AD = [tex]\sqrt{1^2+4^2} = \sqrt{17}[/tex]

Parallel sides have equal slopes:

  • m = - 4 for AB and CD
  • m = - 1/4 for AD and BC

Diagonals are perpendicular as their slopes are negative reciprocal:

  • m = 1 for AC
  • m = -1 for BD

So we see the quadrilateral ABCD has two pairs of parallel sides, all sides are equal and the diagonals are perpendicular.

This is the definition of the rhombus.

View image mhanifa
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