Question

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

Answer 1

The lengths of the segments are DE = 7.28 and RS = 10.77 and they are not congruent

How to determine the length of the segments

From the question, we have the following parameters that can be used in our computation:

The graph

Where, we have

DE = (7, 0) and (0, -2)

RS = (-7, -7) and (3, -3)

The distance and the lengths between the points can be calculated using

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Using the above as a guide, we have the following:

DE = √[(7 - 0)² + (0 + 2)²]

DE = √53

DE = 7.28

RS = √[(-7 - 3)² + (-7 + 3)²]

RS = √116

RS = 10.77

These values are not equal

Hence, the length of the segments are DE = 7.28 and RS = 10.77 and they are not congruent

Answer 2

The answer is below

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|=√((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|=√((0-7)^2+(-2-0)^2)=√(49+4)=√(53)=7.28`

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

`|RS|=√((3-(-7))^2+(-3-(-7))^2)=√(100+16)=√(116)=10.77`

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