Quadrilateral ABCD has vertices A(- 3, 1), B(4, 2) B(4, 2), C(9, - 3) , and D(2, - 4) . aProve that quadrilateral ABCD is a rhombus b )Prove that ABCD is not a square .

Answers

Answer 1

9514 1404 393

Explanation:

The vectors representing the diagonals are ...

  AC = C - A = (9, -3) -(-3, 1) = (12, -4)

  BD = D - B = (2, -4) -(4, 2) = (-2, -6)

The dot-product of these vectors is the sum of the products of corresponding coordinates:

  (12)(-2) +(-4)(-6) = -24 +24 = 0

When the dot-product is zero, the vectors are perpendicular. These vectors are different lengths (BD = 1/2·AC), so they are not the diagonals of a square.

__

The midpoints of the diagonals will be in the same place if the quadrilateral is a rhombus.

  (A +C)/2 = (B +D)/2

We can simplify our effort a bit by multiplying by 2.

  A+C = B+D

  (9, -3) +(-3, 1) = (2, -4) +(4, 2)

  (6, -2) = (6, -2) . . . . . . . . . . . . . . . . yes, the midpoints are the same point

__

We have shown the diagonals of the quadrilateral are different lengths and perpendicular bisectors of each other, so the quadrilateral IS A RHOMBUS, NOT A SQUARE.


Related Questions

Can someone please help me answer this question asap thank you . No links please and thank you .

Answers

It’s a 10 to 1 relationship

Using the formula below, calculate the z-score for the listed data points. z-score: zx = x − μ σ z1 = z5 = z6.5 =

Answers

Answer:

z1 = -1.95

z5 = 0.05

z6.5 = 0.8

Step-by-step explanation:

The value of the z score for a mean of 4 and standard deviation is 1.

What is Z score?

The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (x - μ)/σ

Where x is the raw score, μ is the mean and σ is the standard deviation.

Let us assume that μ = 4, σ = 2, hence for x = 6:

z = (6 - 4) / 2 = 1

The value of the z score for a mean of 4 and standard deviation is 1.

Find out more on Z score at: https://brainly.com/question/25638875

7428.358146 round to nearest cent

Answers

Answer:

7428.40

Step-by-step explanation:

Rob is saving to buy a new MP3 player. For every $16 he earns babysitting, he saves $9. On Saturday, Rob earned $32 babysitting. How much money did he save?



If he earned $32, he saved $____

Answers

Answer:

18 dollars

Step-by-step explanation:

32÷16=2

9×2=18

Rob's office recycled a total of 12 kilograms of paper over 2 weeks. How many weeks will it
take Rob's office to recycle a total of 18 kilograms of paper? Assume the relationship is
directly proportional.
weeks

HOW MANY WEEKS ???

Answers

Answer:

3 unless you're adding onto the 12 kilograms, then only 1

Step-by-step explanation:

In three to five sentences, explain the importance of sentence structures in good writing.

Answers

Answer:

Sentence structure needs to simple, standalone, Grammarly justified and able enough to convey the writer thoughts and feelings clearly

Step-by-step explanation:

Sentence structure is very essential to convey the idea of the writer clearly. It is just like the skeleton of a write up and hence its framework needs to be clear and able enough to express the real sense. The structure of sentence needs to be complete with adequate grammar and punctuations. A good sentence must be able to express a complete idea  on its own.

brainly.com/question/24320025

What is the probability that someone in your class wants the New England Patriots to win

Answers

Answer:

Step-by-step explanation:

It all depends on how many people are in your class.

To calculate probability

Determine a single event with a single outcome.

Identify the total number of outcomes that can occur.

Divide the number of events by the number of possible outcomes.

To determine the probability, Use the formula

What is the formula of probability?

P(A) is the probability of an event “A” n(A) is the number of favourable outcomes. n(S) is the total number of events in the sample space.

P(A | B) = P(A∩B) / P(B)

What is the volume of this pyramid?

Answers

Answer:

150 cm

Step-by-step explanation:

It's 150 cm because if you multiply L x W x H, you will get your answer. So it would be 6 x 5 x 5 = 150.

Please help me out with this I don’t understand it

Answers

Answer:

x = 7.55

Step-by-step explanation:

a = x

b = 8

c = 11

a² + b² = c²

x² + 8² = 11²

x² + 64 = 121

x² = 121 - 64

x² = 57

[tex]\sqrt{x^2} =\sqrt{57}[/tex]

x = 7.5498

Rounded to hundredths:

7.55

Can someone help me with these questions?

Answers

1) 11 books per box with one in the envelope.
2) 44 books are on one shelf. There is 1 book left over.
3) day 9
4) 8 books.

Solve: 16х2 - 81 = 0. (2 points)
Ox = 4, 9
Ox= -4, -9
ООО
9
х=
О
х
81
16
16

HELP PLEASEEE

Answers

C I think I’m sorry if it’s wrong

Answer:

x=9/4,x=-9/4

Step-by-step explanation:

16x^2−81=0

Step 1: Add 81 to both sides.

16x^2−81+81=0+81

16x^2=81

Step 2: Divide both sides by 16.

16x^2/16 = 81/16

x^2 = 81/16

Step 3: Take square root.

x = ±√81/16

x=2.25,x=−2.25

Convert to fraction form.

x=9/4,x=-9/4

The temperature outside changed from 79°F to 44°F over a period of five days. If the temperature changeu
amount each day, what was the daily temperature change?
OA. 35°F
OB. -7°F
ОС.
-35°F
OD. 7°F

Answers

Answer:

B: -7°F

Step-by-step explanation:

79-44=35

Because its over a period of five days we would divide

35÷5=7

Since the numbers are going down its negative

-7

Answer:-7

Step-by-step explanation:

6 1/2 x 3 1/3 x 2

what’s the volume?

Answers

Answer:

1891 /3

Step-by-step explanation:

please help me!! 8th grade math, Pythagorean Theorem

Answers

Answer:

Step-by-step explanation:

-To find the incline do:6^2+14^2=x^2

Than whatever your 6 and 14 equal, find the square root of it

help! brainliest!!! picture below

Answers

the answer to this question is c. which is 18

which question can be answered using the expression 1/3 didvied by 3/4

Answers

Answer:

1/3 divided by 3/4 = 0.44

Step-by-step explanation:

1/3 (0.33) divide by 3/4 (0.75) = 0.44

What is the slope formula?
How do you find slope?

Answers

Answer:

https://www.gstatic.com/education/formulas2/355397047/en/slope_of_a_line.svg

Step-by-step explanation:

To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.

Answer:

cmon bro is not that hard

Step-by-step explanation:

1. Jason bought tickets for him and his friends to
go to the movies. Tickets cost $9 each. He
also spent $15 on food. His total was $51. How
many tickets did he buy for the movie?

Answers

Answer:

he bought 4 tickets

Step-by-step explanation:

51-15=36

36÷9=4

Can I please have Brainliest?

Uehehejjdjdjejjejejjdjdjejejejejejjejejejeejjd

Answers

Answer:

kgkbfkbfbk3grrkmfbhrfikrk

Answer:

thank you for the free point i guess

Step-by-step explanation:

can u mark me brainlest plz

gjnrijnrtibfnsibneifn

What is the volume of the prism, in cubic centimeters?
please help me

Answers

Answer:

4cm ×cmohx9ufochohcohcohc

There is a bag filled with 4 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 blues?

Answers

Answer:

17/55 if simplified otherwise 34/110

Step-by-step explanation:

Answer:

16/81

Step-by-step explanation:

this is the answer that came up on hegarty

solve the system by substitution 3x-y=10 2x=y

Answers

Answer

X=10 and y=20

Step-by-step explanation:

since y=2x, you need to substitute that into the equation to get:

3x-(2x)=10

And evaluate:

x=10

Then substitute 10 into the equation: 2x=y:

2(10)=y

evaluate:

20=y

Now go back to the original equation to check your answer and substitute the values in:

3(10)-(20)=10

30-20=10

10=10

X=10, Y=20
steps
1) substitute 2x into the equation for Y
2) combine like terms ( 3x and -2x which equals 1x or x)
3) solve for x’s value (10)
4) plug in x’s value to solve for y
5) plug values into original equation to check work

Helpppp I need this for rn thank youuuuu❤️

Answers

Answer:

-1,7

0,-3

1,-7

5,47

Step-by-step explanation:

-x-=+

7
-3
-13
-53

This should be right


The following table is from rolling a six sided die 120 times.
Roll 1 2 3 4 5 6
Frequency 15 18 20 17 24 26
What is the experimental probability of rolling anything other than a 2?

Answers

Answer: did you ever get the answer ?

Step-by-step explanation:

Please help me with this

Answers

1 2/4 one and a half

HELP
PLZZZ Z DONT GIVE ME A LINK

Answers

Answer:

These relationships are realted because the variable is multiplied by ten to get the function.

9cm: 90mm

12 1/4cm: 122.5mm

50cm: 500mm

88.49cm: 884.9mm

By the way, can you follow me on Brainly?

Thanks!

Find the CIRCUMFERENCE of a circle with the DIAMETER of 11 ft.
HELP PLS

Answers

Answer:

half of 11 is: 5.5

5.5 x 3.14 x 2 = 34.54

An object is launched directly upward at 64 feet per second from a platform 80 feet high. Write the function for the height of this object at any given time (t seconds).

Answers

Answer: 144 feet

Step-by-step explanation:

What is the value of 4^3

Answers

Answer:

the answer is 64

Step-by-step explanation:

becasue 4 time 4 is 16 and 16 times 4 is 64. You have to multiply 4 against itself 3 times.

Answer:

64

Step-by-step explanation:

4³ = 4 · 4 · 4 = 64

Sinx = [tex]\frac{3}{8}[/tex]
Find cosx and tanx

Answers

Answer:

Cos(x) = sqrt(55) / 8; tan(x) = 3/sqrt(55)

Step-by-step explanation:

Sine is opposite over hypotenuse. So we get that the opposite is 3 and the hypotenuse is 8. To find the adjacent (which we'll need for cosine and tangent), we can use pythagoras' theorem. Therefore, 8^2 = 3^2 + A^2, where A is the adjacent. A then must equal sqrt(64-9) = sqrt(55).

Cosine is adjacent over hypotenuse, which is then sqrt(55) / 8. Tangent is opposite over adjacent, which is then 3 / sqrt(55) or (sqrt55)*3/55

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