Question

The points $(0,0),(0,10),(8,16)$ and $(8,6)$ are joined to form a quadrilateral. Find the type of the quadrilateral.

• A. Rhombus
• B. Square
• C. Rectangle
• D. None of these

Answer 1

Answer: (A)

Rhombus

Let $A(0,0,),B(0,10),C(8,16)$ and $D(8,6)$

Distance formula $=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

Now we are going to find length of sides of quadrilateral.

$AB=\sqrt{(0-0{)}^2+(10-0{)}^2}=\sqrt{100}=10$

$BC=\sqrt{(8-0{)}^2+(16-10{)}^2}=\sqrt{100}=10$

$CD=\sqrt{(8-8{)}^2+(6-16{)}^2}=\sqrt{100}=10$

$DA=\sqrt{(8-0{)}^2+(6-0{)}^2}=\sqrt{100}=10$

Now we are going to find length of diagonal of quadrilateral.

$AC=\sqrt{(8-0{)}^2+(16-0{)}^2}=\sqrt{320}=8\sqrt{5}$

$BD=\sqrt{(8-0{)}^2+(6-10{)}^2}=\sqrt{80}=4\sqrt{5}$

We can see, all sides of quadrilateral are equal but the diagonals are unequal.

$\therefore$ Given quadrilateral is rhombus.