Answered

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)

Verified Answer :

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:

\(\text{slope} = \frac{y_2-y_1}{x_2-x_1}\)

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:

\(AB = \frac{3-(-2)}{-3-(-5)} = \frac{3+2}{-3+5} = \frac{5}{2}\)

Similarly for BC;

\(BC = \frac{5-3}{3-(-3)} = \frac{2}{3+3} = \frac{2}{6}=\frac{1}{3}\)

\(CD = \frac{0-5}{1-3} = \frac{-5}{-2} = \frac{5}{2}\)

and

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

⇒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

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