Mathematics High School

Decide whether ABCD with vertices A (3,8) B (6,5) C (5,4) , and D (2,7) is a rectangle a rhombus or a square

Answers

Answer 1

Given:

The vertices of the quadrilateral ABCD are A(3,8), B(6,5), C(5,4), and D(2,7).

To find:

Whether the given quadrilateral is a rectangle, a rhombus or a square.

Solution:

Distance formula: The distance between two points is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using distance formula, the side lengths are:

[tex]AB=\sqrt{\left(6-3\right)^2+\left(5-8\right)^2}[/tex]

[tex]AB=\sqrt{\left(3\right)^2+\left(-3\right)^2}[/tex]

[tex]AB=\sqrt{9+9}[/tex]

[tex]AB=\sqrt{18}[/tex]

[tex]AB=3\sqrt{2}[/tex]

Similarly,

[tex]BC=\sqrt{\left(5-6\right)^2+\left(4-5\right)^2}=\sqrt{2}[/tex]

[tex]CD=\sqrt{\left(2-5\right)^2+\left(7-4\right)^2}=3\sqrt{2}[/tex]

[tex]AD=\sqrt{\left(2-3\right)^2+\left(7-8\right)^2}=\sqrt{2}[/tex]

The length  of diagonals are:

[tex]AC=\sqrt{\left(5-3\right)^2+\left(4-8\right)^2}=2\sqrt{5}[/tex]

[tex]BD=\sqrt{\left(2-6\right)^2+\left(7-5\right)^2}=2\sqrt{5}[/tex]

From the above calculation, we conclude that the given quadrilateral has two pairs of congruent opposite sides and equal diagonals.

Opposite sides of a rectangle are equal and its diagonals are also equal.

Therefore, the given quadrilateral ABCD is a rectangle.

Related Questions

You should only start the vehicle after you. What?

Answers

Answer:

Buckle your seatbelt

Step-by-step explanation:

Answer:

You should only start the vehicle you should Fasten your seatbelt and make sure that your review mirrors are where you want them to be so you can see the back clearly.

Step-by-step explanation:

Im 17 years old and I been driving a car for a while now and that what my parents told me. Hopefully this helps.

A video game system is on sale for 25% off its original price. If the original price is $340, how much money will be saved?​

Answers

Answer:

85 dollars would be the answer

25% of 340 is 85. Therefor 85 would be your answer

Convert 5 ounces into kilograms. Round your answer to the nearest hundredth.

Answers

Answer:

Answer: 0.141 kilos

0.141748

Step-by-step explanation:

The conversion is 0.1417475 Kg

What is Unit conversion?

Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors which change the measured quantity value without changing its effects.

given:

5 ounces

So, to convert ounces to kilogram we have

1 ounce = 0.0283495 Kg

So, 5 ounces = 5* 0.0283495

5 ounces = 0.1417475 Kg

Hence, 5 ounces = 0.1417475 Kg

Learn more about unit conversion here:

https://brainly.com/question/11543684

#SPJ2

If i went to the store to buy sandwiches should i buy $4.95 for 3 sandwiches or $6.72 for 4 sandwiches what is the best deal?

Explanation why?

Answers

Best deal would be 4.95 for 3 because if you divide the numbers you end up paying more money for the 4 sandwiches. For comparison heres my results
$4.95 for 3 - $1.65 each
$6.72 for 4 - $1.68 each

If AB = 16 inches and AB is dilated by a scale factor of 3/2
find A'B

Answers

Answer:

24 inches

Step-by-step explanation:

16x(3/2)=24

Explain why 21i^2 is equivalent to -21

Answers

Answer:

Step-by-step explanation:

The imaginary number 'i' is equal to the square root of -1. If you were to square the square root, they both cancel and you get -1.

[tex]21i^2=21(\sqrt{-1} )^2=21(-1)=-21[/tex]

Mitzi has 79 coins she divides the coins equally among herself and her 3 brothers Mitzi will keep any coins left over how many coins does each person get

Answers

Answer:

19

Step-by-step explanation:

79÷4=19R3

       ≈ 19

whats 6 divided by 2/3

Answers

Step-by-step explanation:

6 divided by 2/3 is 9

HOPE IT HELPS U

your answer is 9

explanation:

Can somebody help me with this. Will mark brainliest.

Answers

Answer:

15.9

Step-by-step explanation:

4.2r - 12.68 = 10
how to sole it to plz

Answers

r=5.4

4.2r-12.68=10
+12.68 +12.68
4.2r=22.68
4.2/4.2 22.68/4.2
22.68/4.2= 5.4

Hope this helps! Have a great day :)

Hi there!

r=5.4

1.Add the terms:

[tex]22.68*4.2=5.4[/tex]

2.Divide the two terms:

[tex]22.68*4.2=5.4[/tex]

Therefore, r=5.4.

What is the median of this set of values 6,8,10,8,4,2,12

Answers

Median → 8

Mode → 8

Range → 10

Minimum →  2

Maximum → 12

∞God bless you

∞Have an awesome day

Neely has $1.73 in coins. He gives his friend 1 quarter and 3 nickels.
What is the value of the coins he has left?

Answers

Answer:

2.13

Step-by-step explanation:

1.73+.25=1.98

1.98+.15= 2.13

Answer:

1.33

Step-by-step explanation:

A quarter is worth 25 cents so subtract it from $1.73.

1.73 - .25 = 1.48

So then you subtract the 3 nickels which equal 15 cents.

1.73 - .15 = 1.33

So the value left is $1.33.

plz answer only if u know ur correct. tyvm. will give brainliest to best answer

look at the picture

Answers

Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

When x goes up by 1 y goes up by 3

(GIVING BRAINLIEST!!)
Gethyn drinks 48 fluid ounces of water in one day. He needs to drink 8 cups in total. How many more cups does he need to drink?


A) 2 cups
B) 6 cups
C) 384 cups
D) 768 cups

(IF U STEAL POINTS/SAY SOMETHING RANDOM THAT DOESNT HAVE ANYTHING TO DO WITH MY QUESTION ILL REPORT (❁*ᵕ*)︻╦╤─)

Answers

He needs to drink 2 more cups. Explanation: 8 ounces are in 1 cup. He drank 48 fluid ounces of water. 48 ounces of water = 6 cups. He needs to drink 8 cups total. 8-6 = 2.

Answer:

A.) 2 cups

Step-by-step explanation:

kahn academy question please help

Answers

Answer:

1/20

Step-by-step explanation:

[tex] \frac{3}{4} \div \frac{15}{1} \\ \frac{3}{4} \times \frac{1}{15} \\ \frac{3}{60} = \frac{1}{20} [/tex]

Answer:

1/20

Step-by-step explanation:

whats the answer to 3x+4=6x+19

Answers

Answer:

x = -5

Step-by-step explanation:

[tex]3x + 4 = 6x + 19\\-3x + 4 = 19\\-3x = 15\\x = -5[/tex]

3x+4=6x+19 subtract 3x from both sides
4=3x+19 subtract 19 from both sides
-15=3x divide by 3 on both sides
-5=x
The answer is x=-5

Help with this pleaseeeeee!!!!!!!

Answers

Answer:

60

Step-by-step explanation:

V=Base area*height

V=((5*8)/2)*3

V=(40/2)*3

V=20*3

V=60

25+42-47%=?
please help me

Answers

Answer:

The answer is 20!!!

Step-by-step explanation:

Hope this helps :))

help!!!!!!!!!!!!!!!!!!!!!!!!!!! im a dummy

Answers

your scientific notation will be 2.505 x 10^4

Write the number 120 in scientific notation.

Answers

Answer:

The answer is A x 10 b

the answer is 1.2 x 10^2 it gives you 120

can someone please help me, i have a time limit, does anyone know the answer for number 6?!

Answers

Answer:

36.7 I do believe Im not really sure though

Answer:

I believe it is 35.3

180-(90+27)

x/Sin63=18/Sin27

x=18Sin63/Sin27

x=35.3

Please Help!! Fast!!

Answers

Answer:

Use " m-a-t-h-w-a-y " for this.

Step-by-step explanation:

Use the first five terms of the exponential series of ex and a calculator to approximate the value of e^1.36 o the nearest hundredth. a. 3.85 c. 1.65 b. 3.35 d. 1.95

Answers

Answer: a. 3.85

Step-by-step explanation:

In NOP,the measure of p=90 the measure of n=59 and PN=7.4 feet.Find the length of OP to the nearest tenth of a foot

Answers

Answer:

12.3 feet

Step-by-step explanation:

Given

<P = 90 degrees

<N = 59 degrees

PN = 7.4 feet

Required

OP

NO = hypotenuse

OP = adjacent

PN = opposite = 7.4

Using SoH CAH TOA identity

tan <O =PN/OP

tan (180-149) = 7.4/OP

tan 31 = 7.4/OP

OP = 7.4/tan 31

OP = 7.4/0.600

OP = 12.3 feet (to the nearest tenth)

find the vertex of the following equation
y= (x+9)^2+8
​

Answers

(-9,8) is the answer (h,k) is the equation

Write an explicit (function) rule for the sequence 10, 12, 14, 16,...
O f(n) = 8n + 2
O f(n) = 2n +8
O f(n) = 2n + 10
O f(n) = 2n + 6

Answers

Option d is the correct answer

Find the equation of the linear function​

Answers

9514 1404 393

Answer:

  y = -5x -1

Step-by-step explanation:

The 2-point form of the equation for a line can be useful.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (-11 -(-6))/(2 -1)(x -1) +(-6)

  y = -5/1(x -1) -6 . . . . . simplify a bit

  y = -5x -1 . . . . . slope-intercept form


Becca visited 80 vendors at a job fair, and she took a pamphlet from 40% of them. How
many pamphlets did Becca take?

Answers

Answer:

bella in the clouds widhsgnv

Step-by-step explanation:

Write the slope-intercept equation of the line on this graph.

Answers

Answer:

where is the graph?

Step-by-step explanation:

2a + 3b = 5
b = a - 5
How would I solve this ?

Answers

Let me help ya

Step-by-step explanation:

lol I do iready too so first replace the varbile with what ever number they have then you multiply it

5 the answer isieirjjfjriroeoeoeoosodkdkririeje
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