1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Black_prince [1.1K]
4 years ago
12

Verify that parallelogram WXYZ with vertices W(-10, -2), X(-18,12), Y(-2,10), and Z (6,-4) is a rhombus by showing that it is a

parallelogram with perpendicular diagonals.
Mathematics
1 answer:
dusya [7]4 years ago
5 0

The parallelogram WXYZ is a rhombus because its diagonals are perpendicular

Step-by-step explanation:

The product of the slopes of two perpendicular lines is -1, that

means if the slope of one of them is m, then the slope of the

other is \frac{-1}{m}

  • The formula of the slope of a line is m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}
  • (x_{1},y_{1}) and (x_{2},y_{2}) are two points on the line

∵ WXYZ is a parallelogram

∵ W (-10 , -2) , X (-18 , -12) , Y (-2 , 10) , Z (6 , -4)

∵ Its diagonals are WY and XZ

- Find the slope of WY

∵ W = (-10 , -2) and Y = (-2 , 10)

∴ x_{1} = -10 and x_{2} = -2

∴ y_{1} = -2 and y_{2} = 10

∴ m_{WY}=\frac{10--2}{-2--10}=\frac{12}{8}

- Divide up and down by 4 to reduce it to its simplest form

∴ m_{WY}=\frac{3}{2}

- Find the slope of XZ

∵ X = (-18 , 12) and Z = (6 , -4)

∴ x_{1} = -18 and x_{2} = 6

∴ y_{1} = 12 and y_{2} = -4

∴ m_{XZ}=\frac{-4-12}{6--18}=\frac{-16}{24}

- Divide up and down by 8 to reduce it to its simplest form

∴ m_{XZ}=\frac{-2}{3}

∵ (m_{WY}).(m_{XZ})=(\frac{3}{2})(\frac{-2}{3})=\frac{-6}{6}=-1

∴ WY ⊥ XZ

∴ The diagonals of the parallelogram are perpendicular

∴ The parallelogram WXYZ is a rhombus

The parallelogram WXYZ is a rhombus because its diagonals are perpendicular

Learn more:

You can learn more about parallelograms in brainly.com/question/4459688

#LearnwithBrainly

You might be interested in
Crescent Company reported total sales for the current year to be $5,000,000, including cash sales of $1,000,000. Management esti
creativ13 [48]

Answer:

i need points srry

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
At the school store, 3 pens and 2 notebooks cost a total of $12, while 1 pen and 3 notebooks cost a total of $11. This can be re
jasenka [17]

Answer:

D

Step-by-step explanation:

the reason why is because if you put 3 dollars in for the notebooks right you have 3x3=9 and that one pen will be 2 dollars. Now you have 3×2=6 and then the two notebooks will be 6 and you add that and get 12. Hope this helps

3 0
3 years ago
Read 2 more answers
Which polynomial correctly combines the like term and express the given polynomial in standard form
ankoles [38]

Answer:

8mn^5 - 2m^6 + 5m^2n^4 - m^3n^3 + n^6 - 4m^6 + 9m^2n^4 - mn^5 - 4m^3n^3 = -6m^6  - mn^5 - 5m^3n^3 + 14m^2n^4 + 8mn^5  + n^6

Step-by-step explanation:

Given

8mn^5 - 2m^6 + 5m^2n^4 - m^3n^3 + n^6 - 4m^6 + 9m^2n^4 - mn^5 - 4m^3n^3

Required

Correctly combine the like terms

We have:

8mn^5 - 2m^6 + 5m^2n^4 - m^3n^3 + n^6 - 4m^6 + 9m^2n^4 - mn^5 - 4m^3n^3

Collect like terms (in decreasing degrees of m)

- 2m^6 - 4m^6  - mn^5- m^3n^3  - 4m^3n^3+ 5m^2n^4  + 9m^2n^4 + 8mn^5  + n^6

-6m^6  - mn^5 - 5m^3n^3 + 14m^2n^4 + 8mn^5  + n^6

So:

8mn^5 - 2m^6 + 5m^2n^4 - m^3n^3 + n^6 - 4m^6 + 9m^2n^4 - mn^5 - 4m^3n^3 = -6m^6  - mn^5 - 5m^3n^3 + 14m^2n^4 + 8mn^5  + n^6

5 0
3 years ago
Which expression is equivalent to 2^5?
N76 [4]

Answer: 2 x 2 x 2 x 2 x 2

Step-by-step explanation:

This is an exponent so you have the base number which is two and the 5 is how much times to multiply the base number.

Hope that helps!

3 0
3 years ago
Determine which pair of points has a negative slope.
Mashcka [7]
It is C

all the other options have positive slopes


3 0
4 years ago
Other questions:
  • Please help me out with this simple question I REALLY NEED THIS :((((((((
    6·1 answer
  • If f (x) = 4x - 7 and G(x) = 2x + 4 , evaluate f(x) + g(x) for x = -3
    7·1 answer
  • The Brown family's dinner bill was 75.89 and they left 10.00 as a tip. What percent was the tip?
    12·2 answers
  • Write 7 23/100 as a decimal
    11·1 answer
  • My brother is 5 years older than me. My sister is 3 years younger than me. d How old will my sister be when I am n years old?
    12·1 answer
  • Holly has 56 peices of paper and 8 paper clips. If she clips the same amount of paper together with each paper clip, how many pe
    6·1 answer
  • Write the equation of the line parallel to 5x + y = -2 that goes through the point (2, -3).​
    12·1 answer
  • Question 1 of 10
    13·1 answer
  • IUAIUBSHELP PLEASEEA machine in a shoe factory produces shoelaces. The number of shoelaces it produces is proportional to the ti
    15·1 answer
  • Answer questions 10 and 11 based on the information below.
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!