Question

Line segment AB has endpoints (–3.8,–2.7) and (4.3,3.4). Line segment CD has endpoints (8.7,–2.8) and (14.8,5.3). Determine the length of each of these line segments. Then decide whether the two line segments are congruent, and justify your choice. Write your answers with one decimal place.Are the two line segments congruent?Length of line segment AB =Length of line segment CD =

Answer 1

@Mehek14 @escamer

Answer 2

Are you familiar with the distance formula?

Answer 3

This formula

\[\Large d = \sqrt{\left(x_{2}-x_{1}\right)^2+\left(y_{2}-y_{1}\right)^2}\]

Answer 4

not exactly

Answer 5

ok so your first step is to subtract the corresponding x coordinates

in this case, -3.8 and 4.3

I'm focusing on the points (–3.8,–2.7) and (4.3,3.4)

Answer 6

what is -3.8 minus 4.3 equal to?

Answer 7

-8.1

Answer 8

yes

Answer 9

now we square that result to get what?

Answer 10

-65.1

Answer 11

(-8.1)^2 = 65.61

keep in mind that squaring a negative produces a positive result

Answer 12

since negative times negative = positive

Answer 13

ok so we have that result. We need to keep it in mind for later

now we move onto the y coordinates of (–3.8,–2.7) and (4.3,3.4)

we do the same steps

-2.7 minus 3.4 = ???

Answer 14

-6.1

Answer 15

square that to get what?

Answer 16

-37.21

Answer 17

again, remember when you square a negative, you get a positive

Answer 18

(-6.1)^2 = (-6.1)*(-6.1) = +37.21

Answer 19

so 37.21 and 65.1

Answer 20

(-8.1)^2 = 65.61

idk how you're getting 65.1

Answer 21

The two results after squaring are

65.61 (from the x terms)
37.21 (from the y terms)

Answer 22

i was typing it wromg in the calculator.
so
AB= 65.61
CD=37.21

Are they congruent?

Answer 23

we haven't moved to CD yet. We're still on AB

Answer 24

we're not done with AB

Answer 25

ok

Answer 26

ok so we have these two results: 65.61 and 37.21

next step is to add them up

65.61 + 37.21 = 102.82

then finally, the last step is to take the square root of that result

\[\Large \sqrt{102.82} \approx 10.1400197\]

so AB is approximately 10.1400197 units long

Answer 27

Ok.

Answer 28

Recap:

Step 1) Subtract the x coordinates
Step 2) Square the result from step 1
Step 3) Subtract the y coordinates
Step 4) Square the result from step 3
Step 5) Add the results from steps 2 and 4
Step 6) Take the square root from the result of step 5

Answer 29

ok

Answer 30

Tell me what you get for CD

Answer 31

8.1
6.1
65.61
65.61
131.22
17218.68

Answer 32

i mean 11.4

Answer 33

let me check, one moment

Answer 34

you have two copies of 65.61. Double check that part

Answer 35

10.1

Answer 36

Distance from C(8.7,–2.8) and D(14.8,5.3)


Step 1) Subtract the x coordinates
8.7-14.8 = -6.1


Step 2) Square the result from step 1
(-6.1)^2 = 37.21


Step 3) Subtract the y coordinates
5.3 - (-2.8) = 5.3 + 2.8 = 8.1


Step 4) Square the result from step 3
8.1^2 = 65.61


Step 5) Add the results from steps 2 and 4
37.21 + 65.61 = 102.82


Step 6) Take the square root from the result of step 5
\(\Large \sqrt{102.82} \approx 10.1400197\)

so we see that AB = CD because they are the same length. The distance from A to B, is the same as the distance from C to D

Answer 37

btw, you can subtract the x coordinates in any order

notice how
8.7 - 14.8 = -6.1
square that to get 37.21

and how
14.8 - 8.7 = 6.1
square that to get 37.21

The results after squaring the x difference are the same. So that's why you can subtract in any order. The same applies to y as well.

Answer 38

hopefully all this makes sense?

Answer 39

Yes thank you!!!

Answer 40

ok great, you're welcome