Question

Which set of vertices forms a parallelogram?

Answer 1

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

Answer 2

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