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

Question

asked Nov 6, 2019 139k views

2 Answers

Oden · Answer 1 · 2019-11-10T12:50:37+0000

Answer:

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.