Question

50 points
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Answer 1

• Rhombus

Explanation:

Refer to attached

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

• AB= BC = CD = AD =
  `√(1^2+4^2) = √(17)`

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.