Answer:
Options (1), (3) and (5)
Step-by-step explanation:
Coordinates of D → (2, 2)
Coordinates of E → (1, 6)
Coordinates of F → (5, 7)
Coordinates of G → (6, 3)
Length of ED = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
= [tex]\sqrt{(2-1)^2+(2-6)^2}[/tex]
= [tex]\sqrt{17}[/tex]
Length of FG = [tex]\sqrt{(5-6)^2+(7-3)^2}[/tex]
= [tex]\sqrt{17}[/tex]
Length of GD = [tex]\sqrt{6-2)^2+(3-2)^2}[/tex]
= [tex]\sqrt{17}[/tex]
Length of EF = [tex]\sqrt{(1-5)^2+(6-7)^2}[/tex]
= [tex]=\sqrt{17}[/tex]
Since, all sides of the given quadrilateral are equal in length, quadrilateral will be a square.
Therefore, diagonals EG and DF will be perpendicular, equal in measure, congruent and will bisect each other.
Options (1), (3) and (5) are the correct options.
