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lidiya [134]
11 months ago
7

Determine whether quadrilateral ABCD is a rhombus, a rectangle, a square, a parallelogram, or none. List all that apply. Explain

.
--
Help pls? anyone :(?

Mathematics
1 answer:
svlad2 [7]11 months ago
5 0

Answer:

  • ABCD is a rhombus, and a parallelogram

==================================

<h3>Given </h3>

  • Points A(-6, - 1), B(4, - 6), C(2, 5), D(- 8, 10)

First, plot the points (see attached picture).

Then, connect all the points.

<h3>We see that:</h3>

  • Opposite sides are parallel,
  • Diagonals are perpendicular.

From our observation the figure is rhombus.

Let's confirm it with the following.

1) Find midpoints of diagonals and compare.

  • AC → x = (- 6 + 2)/2 = - 2, y = (- 1 + 5)/2 = 2
  • BD → x = (4 - 8)/2 = - 2, y = (- 6 + 10)/2 = 2

The midpoint of both diagonals is same (- 2, 2).

2) Find slopes of diagonals and check if their product is -1, this will confirm they are perpendicular.

  • m(AC) = (5 - (-1))/(2 - (-6)) = 6/8 = 3/4
  • m(BD) = (10 - (-6))/(-8 - 4) = - 16/12 = - 4/3

  • m(AC) × m(BD) = 3/4 * (- 4/3) = - 1

<u>Confirmed.</u>

So this is a rhombus and also a parallelogram but <u>not</u> rectangle or square, since opposite angles are not right angles.

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