Answer:
Square
Step-by-step explanation:
There are different types of quadrilateral,
Kite : a quadrilateral which has two pairs of adjacent equal sides,
Rectangle : a quadrilateral which has two pairs of opposite equal sides and 4 right angles,
Rhombus : a quadrilateral which has equal sides with two pairs of equal opposite angles,
Square : a quadrilateral which has equal sides with 4 right angles,
Trapezoid : a quadrilateral which has one pairs of opposite parallel sides,
Let A≡(1,3), B≡(7,-3), C≡(1,-9) and D≡(-5,-3),
By Distance formula,
[tex]AB=\sqrt{(-3-3)^2+(7-1)^2}[/tex]
[tex]=\sqrt{6^2+6^2}=\sqrt{72}=6\sqrt{2}\text{ unit}[/tex]
Similarly,
[tex]BC=6\sqrt{2}\text{ unit}[/tex]
[tex]CD=6\sqrt{2}\text{ unit}[/tex]
[tex]DA=6\sqrt{2}\text{ unit}[/tex]
Now, the slope of AB,
[tex]m_1=\frac{-3-3}{7-1}=\frac{-6}{6}=-1[/tex]
Similarly,
The slope of BC,
[tex]m_2=1[/tex]
Since, [tex]m_1\times m_2=-1[/tex]
Hence, ∠B = 90°,
Similarly, We can obtain,
∠A = ∠C = ∠D = 90°
Therefore, By the above definitions it is clear that ABCD is a square.
