Answer:
The answer is below
Step-by-step explanation:
The complete question is contained in the image.
The distance between points [tex]A(x_1,y_1)[/tex] and [tex]B(x_2,y_2)[/tex] in the coordinate plane is given as:
[tex]|AB|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Point D is at (7, 0) and E at (0, -2) hence the distance between the two points is:
[tex]|DE|=\sqrt{(0-7)^2+(-2-0)^2}=\sqrt{49+4}=\sqrt{53}=7.28[/tex]
Point R is at (-7, -7) and S at (3, -3) hence the distance between the two points is:
[tex]|RS|=\sqrt{(3-(-7))^2+(-3-(-7))^2}=\sqrt{100+16}=\sqrt{116}=10.77[/tex]
Since |RS| ≠ |DE|, therefore they are not congruent
