Question

Fill in the blanks using the available answer choices. The vertices of a quadrilateral are A(–3, 1) , B(4, 2) , C(9, –3) and D(2, –4) . Complete the statement to best classify what type of quadrilateral ABCD is. In quadrilateral ABCD , have equal length and there are right angles, so ABCD is best classified as a .

Answer 1

Quadrilateral ABCD can be best classified as a square due to equal side lengths and right angles.

Step-by-step explanation:

In quadrilateral ABCD, we can calculate the lengths of the four sides using the distance formula.

AB = sqrt((4 - (-3))^2 + (2 - 1)^2) = sqrt(49 + 1) = sqrt(50)

BC = sqrt((9 - 4)^2 + (-3 - 2)^2) = sqrt(25 + 25) = sqrt(50)

CD = sqrt((2 - 9)^2 + (-4 - (-3))^2) = sqrt(49 + 1) = sqrt(50)

AD = sqrt((2 - (-3))^2 + (-4 - 1)^2) = sqrt(25 + 25) = sqrt(50)

Since all four sides of the quadrilateral have equal lengths (AB = BC = CD = AD) and there are right angles, quadrilateral ABCD can be best classified as a square.