Question

Find the length of the given segments and determine if they are congruent Simplify DE and RS

Answer 1

Answer:

The answer is below

Step-by-step explanation:

The complete question is contained in the image.

The distance between points $A(x_1,y_1)$ and $B(x_2,y_2)$ in the coordinate plane is given as:

$|AB|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Point D is at (7, 0) and E at (0, -2) hence the distance between the two points is:

$|DE|=\sqrt{(0-7)^2+(-2-0)^2}=\sqrt{49+4}=\sqrt{53}=7.28$

Point R is at (-7, -7) and S at (3, -3) hence the distance between the two points is:

$|RS|=\sqrt{(3-(-7))^2+(-3-(-7))^2}=\sqrt{100+16}=\sqrt{116}=10.77$

Since |RS| ≠ |DE|, therefore they are not congruent