Question

The coordinates of a quadrilateral are (1,3),(7-3),(1,-9) , and (-5,-3). What shape is formed? Select all that apply

Answer 1

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,

$AB=\sqrt{(-3-3)^2+(7-1)^2}$

$=\sqrt{6^2+6^2}=\sqrt{72}=6\sqrt{2}\text{ unit}$

Similarly,

$BC=6\sqrt{2}\text{ unit}$

$CD=6\sqrt{2}\text{ unit}$

$DA=6\sqrt{2}\text{ unit}$

Now, the slope of AB,

$m_1=\frac{-3-3}{7-1}=\frac{-6}{6}=-1$

Similarly,

The slope of BC,

$m_2=1$

Since, $m_1\times m_2=-1$

Hence, ∠B = 90°,

Similarly, We can obtain,

∠A = ∠C = ∠D = 90°

Therefore, By the above definitions it is clear that ABCD is a square.

Answer 2

Kite. The other answers don't fit the criteria.