Answer:
1st Option is correct.
Step-by-step explanation:
Given:
Vertices of the quadrilateral ABCD.
A( -5 , -1 ) , B( -5 , 3 ) , C( -2 , 3 ) , D( -2 , -1 )
To find: Name of the Quadrilateral.
We use Distance formula to find the length of the sides and diagonal of the Quadrilateral.
Distance between two point = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Length of Side AB [tex]=\sqrt{(-5-(-5))^2+(-1-3)^2}=\sqrt{(0)^2+(-4)^2}=\sqrt{0+16}=4[/tex]
Length of Side CB [tex]=\sqrt{(-2-(-5))^2+(3-3)^2}=\sqrt{(-2+5)^2+(0)^2}=\sqrt{9+0}=3[/tex]
Length of Side CD [tex]=\sqrt{(-2-(-2))^2+(-1-3)^2}=\sqrt{(0)^2+(-4)^2}=\sqrt{0+16}=4[/tex]
Length of Side AD [tex]=\sqrt{(-2-(-5))^2+(-1-(-1))^2}=\sqrt{(3)^2+(0)^2}=\sqrt{9+0}=3[/tex]
Length of the Diagonal AC [tex]=\sqrt{(-2-(-5))^2+(3-(-1))^2}=\sqrt{(3)^2+(4)^2}=\sqrt{9+16}=5[/tex]
Length of the Diagonal BD [tex]=\sqrt{(-2-(-5))^2+(-1-3)^2}=\sqrt{(3)^2+(-4)^2}=\sqrt{9+16}=5[/tex]
So, Opposite side of the Quadrilateral are Equal that is AB = CD = 4 unit and CB = AD = 3 unit
Also, Diagonals are equal that is AC = BD = 5 unit
⇒ Quadrilateral is a RECTANGLE.
Therefore, 1st Option is correct.
