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Which set of vertices forms a parallelogram?


A(2, 4), B(3, 3), C(6, 4), D(5, 6)



A(-1, 1), B(2, 2), C(5, 1), D(4, 1)



A(-5, -2), B(-3, 3), C(3, 5), D(1, 0)



A(-1, 2), B(1, 3), C(5, 3), D(1, 1)

Respuesta :

AskMRShawnLove
A(-5, -2), B(-3, 3), C(3, 5), D(1, 0 is the correct answer.so for answering it late

Answer:

Option 3rd is correct

A(-5, -2), B(-3, 3), C(3, 5), D(1, 0) set of vertices forms a parallelogram

Step-by-step explanation:

Slope formula is given by:

[tex]\text{slope} = \frac{y_2-y_1}{x_2-x_1}[/tex]

Properties of the parallelogram:

  • Opposite sides are equal and parallel.
  • Diagonals are unequal
  • Slope of the opposite sides are equal.
  • Opposite angles are equal.

Consider the set of vertices:

A(-5, -2), B(-3, 3), C(3, 5), D(1, 0)

Apply the slope formula:

[tex]AB = \frac{3-(-2)}{-3-(-5)} = \frac{3+2}{-3+5} = \frac{5}{2}[/tex]

Similarly for BC;

[tex]BC = \frac{5-3}{3-(-3)} = \frac{2}{3+3} = \frac{2}{6}=\frac{1}{3}[/tex]

[tex]CD = \frac{0-5}{1-3} = \frac{-5}{-2} = \frac{5}{2}[/tex]

and

[tex]AD= \frac{0-(-2)}{1-(-5)} = \frac{0+2}{6} = \frac{2}{6}=\frac{1}{3}[/tex]

⇒Slope of AB =Slope of CD and Slope of BC = Slope of AD

By property of parallelogram:

⇒A(-5, -2), B(-3, 3), C(3, 5), D(1, 0) set of vertices forms a parallelogram