Name the figure formed by the points $A (9,\ 0),\ B (9,\ 6),\ C (–9,\ 6)$ and $D(–9,\ 0)$.

Given: Points $A (9,\ 0),\ B (9,\ 6),\ C (–9,\ 6)$ and $D(–9,\ 0)$

To do: To find the name of the figure formed by the given points.

Solution:

On using the distance formula,

Distance between the two points$=\sqrt{( x_2-x_1)^2+( y_2-y_1)^2}$

$AB=\sqrt{( 9-9)^2+( 6-0)^2}$

$\Rightarrow AB=6$

$BC=\sqrt{( -9-9)^2+( 6-6)^2}$

$\Rightarrow BC=18$

$CD =\sqrt{( -9+9)^2+( 0-6)^2}$

$\Rightarrow CD=6$

$DA=\sqrt{(-9-9)^2+(0-0)^2}$

$\Rightarrow DA=18$

So, it's opposite sides are equal, hence it is rectangle.

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Updated on: 10-Oct-2022

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