Question

What is the most precise name for quadrilateral ABCD with vertices A(-4,-1) B(-2,-5), C(4, -2) and D(2,2)?

A( parallelogram
B( rhombus
C( quadrilateral
D( rectangle

Answer 1

Quadrilateral ABCD with vertices A(-4,-1) B(-2,-5), C(4, -2) and D(2,2) is a parallelogram. So the correct option is A.

Step-by-step explanation:

Quadrilateral ABCD with vertices A(-4,-1) B(-2,-5), C(4, -2) and D(2,2) is a parallelogram.

A parallelogram is a quadrilateral with opposite sides that are parallel. In this case, if we find the slopes of the opposite sides AB and CD, we can see that they are equal: slope AB = (-5-(-1))/(-2-(-4)) = -4/2 = -2, slope CD = (2-(-2))/(4-2) = 4/2 = 2. Therefore, AB and CD are parallel. Similarly, we can find that the slopes of sides BC and AD are equal, making them parallel as well.

Answer 2

(A) Parallelogram

Step-by-step explanation:

The given coordinates of quadrilateral ABCD are A(-4,-1) B(-2,-5), C(4, -2) and D(2,2), using the distance formula, the sides are

AB=
`√((-5+1)^2+(-2+4)^2)=√(16+4)=√(20)`,

BC=
`√((-2+5)^2+(2+4)^2)=√(9+36)=√(45)`

CD=
`√((-2-2)^2+(4-2)^2)=√(16+4)=√(20)`

DA=
`√((2+1)^2+(2+4)^2)=√(9+36)=√(45)` and diagonals are:

AC=
`√((-2+1)^2+(4+4)^2)=√(1+64)=√(65)` and

BD=
`√((-5-2)^2+(-2-2)^2)=√(49+16)=√(65)`

Since, the opposite sides of the given quadrilateral that are )AB and DC) and (BC and DA) are equal, moreover the diagonals are also congruent.

thus, by the definition of rectangle, that the opposite sides are equal and diagonals are congruent, the given quadrilateral is rectangle.