The diagonals of quadrilateral EFGH intersect at D(3,3). EFGCH has vertices at E(4,7) and F(-3,5). What must be the coordinates of G and H to ensure that EFGH is a parallelogram.

Answers

Answer 1

Answer:

[tex]G = (2,-1)[/tex]

[tex]H = (9,1)[/tex]

Step-by-step explanation:

Given

[tex]E = (4,7)[/tex]

[tex]F=(-3,5)[/tex]

[tex]D =(3,3)[/tex] --- Diagonal

Required

Determine the coordinates of G and H

Since EFGH is a parallelogram, then:

D is the midpoint of EG and EF

For EG, we have:

[tex](3,3) = \frac{1}{2}(4 + x,7+y)[/tex]

Where x, y are the coordinates of G.

Multiply both sides by 2

[tex](6,6) = (4+x,7+y)[/tex]

By comparison:

[tex]4 + x = 6[/tex] ==> [tex]x =2[/tex]

[tex]7 + y= 6[/tex] ==> [tex]y = -1[/tex]

So:

[tex]G = (2,-1)[/tex]

For FH, we have:

[tex](3,3) = \frac{1}{2}(-3 + x,5+y)[/tex]

Where x, y are the coordinates of H.

Multiply both sides by 2

[tex](6,6) = (-3 + x,5+y)[/tex]

By comparison:

[tex]-3+x = 6[/tex] ==> [tex]x = 9[/tex]

[tex]5 + y = 6[/tex] ==> [tex]y =1[/tex]

So:

[tex]H = (9,1)[/tex]


Related Questions

What type of function has the possibility of two x-intercepts?
I. Linear
II. Quadratic
III. Absolute Value

Answers

Answer:-
I think it’s Quadratic, since as in a quadratic equation:
ax^2 + bx + c = 0

A quadratic function has the possibility of two x-intercepts.

What is a quadratic function?

A quadratic function is one of the form f(x) = ax² + bx + c, where a, b, and c are numbers with a not equal to zero.

Given that a function having two x-intercepts

The graph of a quadratic function will always have one y-intercept and can have as many as two x-intercept.

Hence, a quadratic function has the possibility of two x-intercepts.

For more references on a quadratic function, click;

https://brainly.com/question/27958964

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AYUDAAAA AYUDAAAA NO ME ACUERDOOOOO AYUDAAA
2+5(520)÷8

Answers

anade 2 mas 5 multiplicow por 520 dividido por 8

Answer:

327

Step-by-step explanation:

2+5x520 divide by 8

2+325=327

Pls give brianly if its correct?

What’s a function with a slope of 4 that includes the point a (- 1, 3)? I need an equation

Answers

Use y=mx+b then you will be able to get your equation.

Which function IS graphed below?

Answers

Answer:

first you write your full question then ,i will try.

Step-by-step explanation:

please give me brain list and follow

i need to find the area but i don’t know the steps

Answers

I’m not sure but I think it is 24

Answer:

48in2

Step-by-step explanation:

1/2 × (11.9+4.1) ×6= 48in2

Find the quotient of 1 1/4 and 3 1/2 express your answer in simplest form

Answers

Answer:

11/14

Step-by-step explanation:

11/4 / 3 1/2

3 1/2= 3*2+1= 6+1=7/2

11/4 * 2/7= 22/28

22/2=11

28/2= 14

11/14

11/14 is the answer! (Quotient in simplest form)

what ratio is equivalent to 6 out of 15

Answers

Answer:

40%

Step-by-step explanation:

Answer:

2:5

Step-by-step explanation:

6/15 divided by 3/3 = 2/5

2/5 is the most simplified it can get

2:5

I NEED UR HELP ASAP!! PLEASE

Answers

Answer:

4 inches

Step-by-step explanation:

To solve this, use the Pythagorean Theorem: a² + b² = c². You insert the measurements you have: 3² + b² = 5² or 9 + b² = 25. To solve this, subtract 9 from both sides: b² = 16. To solve for b (length) specifically, find the square root of 16: 4.

Hope it helps!

A video game box is 15 inches long and 10
inches wide. If the volume of the box is 750
cubic inches, how tall is the box?
in inches

Answers

Answer:

The box is 5 inches tall

Step-by-step explanation:

The given dimensions of the video games are;

The length of the video game, L = 15 inches

The width of the video game, W = 10 inches

The volume of the video game box, V = 750 cubic inches

Assuming that the shape of the video game box is a cuboid, we have;

The formula for the volume of a cuboid, V = Length, L × Width, W × Height, H

∴ V = L × W × H

The height of the cuboid, H = V/(L × W)...(1)

Where, for the video game box;

L = Length = 15 in.

W = Width = 10 in.

V = Volume = 750 in.³

Plugging in the values of the variables in equation (1) gives;

H =  V/(L × W) = 750 in.³/(15 in. × 10 in.) = 5 in.

The height of the box, H = 5 inches.

When tossing three coins, what is the probability of tossing exactly two tails?

Answers

Answer:

1/3?

Step-by-step explanation:

Answer:OK SO Since the outcome of a coin toss is equiprobable, the probability of getting exactly two tails out of three is equal to the number of ways to get two tails out of three - aka - divided by the total number of possible coin flip outcomes - aka . Ergo, 3/8 is the probability.

hope this helps have a nice day❤️

Step-by-step explanation:

If the endpoints of the diameter of a circle are (6, -2)and (-6 ,2)what is the standard form equation of the circle

Answers

Answer:

[tex]x^2 + y^2 - 40 = 0[/tex]

Step-by-step explanation:

Given

[tex](h_1,k_1) = (6,-2)[/tex]

[tex](h_2,k_2) = (-6,2)[/tex]

Required

Determine the equation of the circle

First, calculate the midpoint of the given coordinates:

[tex](h,k) = \frac{1}{2}(h_1+h_2,k_1+k_2)[/tex]

[tex](h,k) = \frac{1}{2}(6-6,-2+2)[/tex]

[tex](h,k) = \frac{1}{2}(0,0)[/tex]

[tex](h,k) = (0,0)[/tex]

Next, calculate the radius.

This is the distance between [tex](0,0)[/tex] calculated above and any of [tex](6,-2)[/tex] [tex](-6,2)[/tex]

Using:

[tex](0,0)[/tex] and [tex](-6,2)[/tex], the radius is:

[tex]r = \sqrt{(0 - (-6))^2 + (0-2)^2}[/tex]

[tex]r = \sqrt{40}[/tex]

The equation is then calculated using:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

Where:

[tex]r = \sqrt{40}[/tex] and [tex](h,k) = (0,0)[/tex]

[tex](x - 0)^2 + (y - 0)^2 = (\sqrt{40})^2[/tex]

[tex](x )^2 + (y)^2 = 40[/tex]

[tex]x^2 + y^2 = 40[/tex]

[tex]x^2 + y^2 - 40 = 0[/tex]

A circular plate has circumference 16.3 inches. What is the area of this plate?

Answers

Answer: Circumference:  C = 2πr = 16.3

2(3.14)r = 16.3

r = 16.3/6.28

r = 2.5955414

Area:  A = πr2

A = 3.14(2.5955414)2

A = 21.15366242 in2

Rounded to nearest whole number the area is 21 in2

Step-by-step explanation:

* Lets revise some rules of a circle

- The circumference of a circle = 2πr , where r is the radius of it

- The area of the circle = πr²

* Lets solve the problem

∵ A circular plate has circumference 16.3 inches

∵ The circumference = 2πr

∵ π = 3.14

- Lets find the radius of the plate

∵ 16.3 = 2(3.14)r

∴ 16.3 = 6.28r

- Divide both sides by 6.28

∴ r = 16.3/6.28 = 2.5955 ≅ 2.6

∴ The radius of the plate is 2.6 inches

* Lets find the area of the plate

∵ The area = πr²

∵ π = 3.14

∵ 4 = 2.6

∴ The area = 3.14(2.6)² = 21.22 ≅ 21

* The area of the plate is 21 inches

Answer:

Step-by-step explanation:

r is the radius

Circumference = 2πr = 16.3

r = 16.3/(2π) = 8.15/π

Area = πr² = π(8.15/π)² = 8.15²/π ≈ 21.1 sq in

help pls need help before my daughter pls and thank you ​

Answers

Answer:

I would say line d

Step-by-step explanation:

its the line of best fit (has the most points going through it)

Caroline is going to invest $5,500 and leave it in an account for 10 years. Assuming
the interest is compounded continuously, what interest rate, to the nearest tenth of a
percent, would be required in order for Caroline to end up with $10,100?

Answers

Answer:

6.1

Step-by-step explanation:

I just know

Use the equation w=9b to find the value of w when b=6.

Answers

9 x 6 = 54 so w= 54 .............

I Need help now!!!!

Answers

Answer:

The answer is B.x2/4y3n hope it helps

NEED HELP WILL GUVE 5 stars

Answers

Answer:

m=15

Step-by-step explanation:

m/9 + 2/3    

          x 3                         7/3  x 3 =  21/9

m/9 + 6/9 = 21/9

21-6=15

15/9 + 6/9 = 21/9 = 7/3

Pls, help. Whichever one you want, but whoever does all of them first I will give them the brainiest.

Answers

Answer:

what am i supposed to help with??

Step-by-step explanation:

In parallelogram FGHJ

Answers

120° + x = 180°
x = 60°

Given that f(x) = 2x − 5, find the value of x that makes f(x) = 15.
Group of answer choices

20

25

5

10
Plzz help asap!!!

Answers

Answer:

25

Step-by-step explanation:

so you replace all the x's with 15 and it becomes

2×15-5

2×15=30

30-5=25

if f(x)=10(2) then which of the following represents the value of f (0)

Answers

Answer:

< x < 10

Step-by-step explanation:

that answer would be

what is the opposite of -2​

Answers

Answer:

2

Step-by-step explanation:

opposite of -2 is 2 because it is like 2 is opposite of -2

Answer:

2.

Step-by-step explanation:

The opposite of a number is the number which when added to it gives a result of zero.

-2 + 2 = 0 so the required  number is  2.

Please solve quickly! Qestion: c - 1.5 = 7

Answers

Answer:

8.5

Step-by-step explanation:

c = 8.5

hope this helps

Answer:8.5

Step-by-step explanation:

Add 7 and 1.5

Help on this question

Answers

Answer:

126 minutes, or 2.1 hours.

Step-by-step explanation:

Change 6 hours to minutes. (6x60=360)

Find 1% of 360 (360x0.01=3.6)

Multiply 3.6 to 20 (cleaning) and then multiply 3.6 to 15 (video games)

Then, add them, which you should get the answer of 126.

Which is the simplified form of the expression 6y – 4 + 3y?

Answers

Hello!    

3y^1-1

3y^0

3*1

3

y=3

Which of the following number sentences show the correct method to find 43% of 59 Select TWO that apply.

A)43 x 59

B)43/100 x 59

C)0.43 x 59

D)0.43 x 0.59

Answers

Answer:

a and b

Step-by-step explanation:

please help on this i cant understand it

Answers

Answer:

to get the probability you add the number of figure all together

divide the number of spheres with the total

ie

2 ÷ 10

you get 1÷ 5

you get the answer as 0.2

∠A and \angle B∠B are vertical angles. If m\angle A=(4x-13)^{\circ}∠A=(4x−13)

and m\angle B=(3x+19)^{\circ}∠B=(3x+19)

, then find the measure of \angle A∠A.

Answers

Answer:

m∠A=  115

Step-by-step explanation:

The required measure of the angle A is 115°.

Given that,
Two corresponding equal angles are given,
A = 4x - 13 and B = 3x + 19 all are in degrees.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

What is the angle?

The angle can be defined as the one line inclined over another line.

Here,
A = 4x - 13

B = 3x + 19

A = B
4x - 13 = 3x + 19
4x - 3x = 19 + 13
x = 32


Now the measures,
A = 4x -13

A = 4 * 32 - 13
A = 128 - 13
A = 115

Thus, the required measure of the angle A is 115°.

Learn more about simplification here: https://brainly.com/question/12501526

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Solve this equation:
7x - [5 + (3x - 2)] = x - (4x - 5) + (2x - 1)

Answers

Answer:

x = 7/5

I hope this helps

Step-by-step explanation:

7x - [5 + (3x - 2)] = x - (4x - 5) + (2x - 1)

7x - 5 -3x +2 = x -4x +5 +2x -1

4x -3 = -x +4

4x +x = 4+3

5x = 7

x = 7/5

HURYY THIS IS WORTH ALOT I’ll make brainlist

Answers

Answer:

B.4

Step-by-step explanation:

NASAGUTAN KO YAN TAMA AKO

The answer is number 2
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