Question

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)

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

Option 3rd is correct

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

Explanation:

Slope formula is given by:

`\text{slope} = (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 = (3-(-2))/(-3-(-5)) = (3+2)/(-3+5) = (5)/(2)`

Similarly for BC;

`BC = (5-3)/(3-(-3)) = (2)/(3+3) = (2)/(6)=(1)/(3)`

`CD = (0-5)/(1-3) = (-5)/(-2) = (5)/(2)`

and

`AD= (0-(-2))/(1-(-5)) = (0+2)/(6) = (2)/(6)=(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