Answer:
The area of Rectangle with given vertices is 6 unit ²
Step-by-step explanation:
Given points of vertices of rectangle as :
A = ( - 4, 0)
B = ( - 3 , 1)
C = ( 0 , - 2)
D = ( - 1 , - 3)
Now the measure of side AB = [tex]\sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}}[/tex]
So, AB = [tex]\sqrt{( - 3 + 4)^{2} + (1 - 0)^{2}}[/tex]
AB = [tex]\sqrt{2}[/tex] unit
The measure of side BC = [tex]\sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}}[/tex]
BC = [tex]\sqrt{(0 +3)^{2} + (- 2 - 1)^{2}}[/tex]
BC = 3[tex]\sqrt{2}[/tex] unit
The measure of side CD = [tex]\sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}}[/tex]
CD = [tex]\sqrt{( - 1 - 0)^{2} + ( - 3 + 2)^{2}}[/tex]
CD = [tex]\sqrt{2}[/tex] unit
The measure of side DA = [tex]\sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}}[/tex]
DA = [tex]\sqrt{(- 4 + 1)^{2} + (0 + 3)^{2}}[/tex]
DA = 3[tex]\sqrt{2}[/tex] unit
So, the measure of side AB = The measure of side CD = [tex]\sqrt{2}[/tex] unit
And The measure of side BC = The measure of side DA = 3[tex]\sqrt{2}[/tex] unit
So, Let Length = AB = CD
And Width = BC = DA
∴ The area of Rectangle = Length × Width unit²
Or, The area of Rectangle = AB × BC
So, The area of Rectangle = [tex]\sqrt{2}[/tex] unit × 3[tex]\sqrt{2}[/tex] unit
∴ The area of Rectangle = 6 unit ²
Hence The area of Rectangle with given vertices is 6 unit ² Answer
