Question

Rectangle ABCD is graphed in the coordinate plane.The following are the vertices of the rectangle:A(-2,1),B(3,2),C(3,4),and D(-2,4), what is the perimeter of rectangle ABCD

Answer 1

Answer:

Therefore,

$\textrm{Perimeter of rectangle}=14\ cm$

Step-by-step explanation:

Given:

Rectangle ABCD

vertices of the rectangle:

A(-2,2),

B(3,2),C(3,4),and D(-2,4),

Let,

Length of Rectangle be AB and Width be BC

To Find:

Perimeter of rectangle ABCD  = ?

Solution:

We Know ,

$\textrm{Perimeter of rectangle}=2(Length + Width)$

Lets find length and width by Distance Formula,

$l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}$

On substituting the values we get

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

$l(AB) = \sqrt{((5)^{2}}=5\ units$

Similarly,

$l(BC) = \sqrt{((3-3)^{2}+(4-2)^{2} )}$

$l(BC) = \sqrt{4}=2\ units$

Now substituting  AB and BC in Perimeter Formula we get

$\textrm{Perimeter of rectangle}=2(AB + BC)=2(5+2)=2\times 7=14\ cm$

Therefore,

$\textrm{Perimeter of rectangle}=14\ cm$

Note Here Vetex A is wrong the correct on is A(-2 ,2)