Question

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

Kite
Rectangle
Rhombus
Square
Trapezoid

Answer 1

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

Answer 2

Square

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=√((-3-3)^2+(7-1)^2)`

`=√(6^2+6^2)=√(72)=6√(2)\text{ unit}`

Similarly,

`BC=6√(2)\text{ unit}`

`CD=6√(2)\text{ unit}`

`DA=6√(2)\text{ unit}`

Now, the slope of AB,

`m_1=(-3-3)/(7-1)=(-6)/(6)=-1`

Similarly,

The slope of BC,

`m_2=1`

Since,
`m_1* 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.