Question

Select the correct answer.

Which set of vertices forms a parallelogram?

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

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

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

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

Answer 1

Explanation:

Option 3 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:

slope = y2-y1

over x2-x1

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)

⇒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

Answer 2

Answer: OPTION C.

Explanation:

A parallelogram is defined as a quadrilateral which has two pairs of parallel sides.

Attached is shown in the parallelogram obtained by plotting the vertices provided in Option C.

If that figure is a parallelogram, then:

`Slope\ AB=Slope\ CD\\\\Slope\ BC=Slope\ AD`

Let's check this:

`Slope\ AB=(-2-3)/(-5-(-3))=(5)/(2)`

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

`Slope\ BD=(3-5)/(-3-3)=(1)/(3)`

`Slope\ DA=(-2-0)/(-5-1)=(1)/(3)`

Therefore, the set of vertices that forms a parallelogram is:

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