Question

Quadrilateral ABCD has coordinates (3, 1), (4, 4), (7, 5), (6, 2). Quadrilateral ABCD is a
Answer

square because its length and width are both square root of 10 units and adjacent sides are perpendicular

rhombus because its length and width are both square root of 10 units and adjacent sides are not perpendicular

rectangle because its length is two times the square root of 10 units, its width is square root of 10 units, and adjacent sides are perpendicular

trapezoid because it has only one pair of parallel sides

Answer 1

D:??

Answer 2

A(3,1) C(7,5)
B(4,4) D(6,2)

Distance between two coordinates-
\[\sqrt{(x_{2}-x_{1})^{2}+y_{2}-(y_{1})^{2}}\]

therefore, \[\huge AB=\sqrt{(3-4)^2+(1-4)^{2}}=\sqrt{1+9}=\sqrt{10}\]
\[\huge BC=\sqrt{(4-7)^2+(4-5)^{2}}=\sqrt{1+9}=\sqrt{10}\]
\[\huge CD=\sqrt{(7-6)^2+(5-2)^{2}}=\sqrt{1+9}=\sqrt{10}\]
\[\huge AD=\sqrt{(3-6)^2+(1-2)^{2}}=\sqrt{1+9}=\sqrt{10}\]
\[\huge AC=\sqrt{(3-7)^2+(1-5)^{2}}=\sqrt{16+16}=\sqrt{32}\]
\[\huge BD=\sqrt{(4-6)^2+(4-2)^{2}}=\sqrt{4+4}=\sqrt{8}\]

Since, In quadrilateral ABCD, AB=BC=CD=AD, and diagonals AC and BD are not equal,therefore it is a rhombus.

Answer 3

So which one would it be?

Answer 4

2nd.

Answer 5

Thank you a lot (:

Answer 6

:)