Mathematics High School

PLZ HELP -geometry- Find the coordinates of the intersection of the diagonals of parallelogram GHJK with vertices G(1,3), H(4,3), J(5,1), and K(2,1).

The coordinates are ( , ).

Answers

Answer 1

Answer:

The coordinates of the intersection of the diagonal of the parallelogram are [tex]M(x,y) = (3,2)[/tex].

Step-by-step explanation:

Diagonals are represented by line segments GJ and KH. Since quadrilateral is a parallelogram, then coordinates of the intersection are located at midpoint of each diagonal ([tex]M(x,y)[/tex]). That is:

[tex]M(x,y) = G(x,y) + \frac{1}{2}\cdot \overrightarrow {GJ}[/tex]

[tex]M(x,y) = G(x,y) +\frac{1}{2}\cdot [J(x,y)-G(x,y)][/tex] (1)

If we know that [tex]G(x,y) = (1,3)[/tex] and [tex]J(x,y) = (5,1)[/tex], the coordinates of the intersection of the diagonals of the parallelogram are:

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

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

[tex]M(x,y) = (1,3) +(2,-1)[/tex]

[tex]M(x,y) = (3,2)[/tex]

There is another form:

[tex]M(x,y) = K(x,y) +\frac{1}{2}\cdot \overrightarrow{KH}[/tex]

[tex]M(x,y) = K(x,y) + \frac{1}{2}\cdot [H(x,y)-K(x,y)][/tex] (2)

If we know that [tex]K(x,y) = (2, 1)[/tex] and [tex]H(x,y) = (4,3)[/tex], the coordinates of the intersection of the diagonals of the parallelogram are:

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

[tex]M(x,y) = (2,1) + \frac{1}{2} \cdot (2,2)[/tex]

[tex]M(x,y) = (2,1) + (1,1)[/tex]

[tex]M(x,y) = (3,2)[/tex]

Therefore, the coordinates of the intersection of the diagonal of the parallelogram are [tex]M(x,y) = (3,2)[/tex].

Related Questions

what is the first step to solving 9z-21=60​

Answers

add 21 to both sides, so you get 9z = 81

Answer:

add 21 to both sides

Step-by-step explanation:

9z-21=60

9z-21+21 =60+21

9z=81

9z/9=81/9

z = 9

Noah ran 54 miles in 9 days.The graph relating Greta’s total distance to the number of days passes through the points (0,0) and (5,45).Who ran more miles per day?

Answers

Answer: Noah ran more miles

Step-by-step explanation:

Pleaseee helppp answer correctly !!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!

Answers

Answer:

perimeter of any figure can be define the sum of all sides.

perimeter of the figure=33.4ft + 6.5ft + 9ft + 9ft + 9ft + 6.5ft + 7.7ft + 16.7ft

perimeter of the figure=97.8 ft.

Malala is following this recipe for bread rolls.
She uses 500 mL of water.
How much of each of the other ingredients does she use?

Recipe: Makes 15 bread rolls
480 g flour
12 g salt
6 g yeast
30 mL oil
600 mL water

Answers

Answer:

500ml water

400 g flour

2 g salt

5 g yeast

25ml oil

Step-by-step explanation:

Gary is building a new L-shaped desk for his room. He wants to make sure it
is large enough to hold all his supplies. The dimensions of the desk, in feet,
are shown in the diagram. What is the area of the desk?
9 ft
2 ft
6 ft
6 ft
4 ft
3 ft
A. 24 square feet
B. 36 square feet
C. 30 square feet
D. 54 square feet

Answers

Answer:

30ft2.  so its c

Step-by-step explanation:

its 30

quiz verified

Can someone please help me with my math corrections?​

Answers

Answer:

Step-by-step explanation:

y = 2x + 3         {y = mx + b}

In Function A, rate of change is 2

Function B:

Rate of change = Change in y÷ change in x

                         [tex]= \frac{11-7}{0-[-1]}\\\\=\frac{11-7}{0+1}\\\\=\frac{4}{1}\\\\= 4[/tex]

In function B, rate of change is 4

Least: Function A

Greatest: Function B

Mr. Greene
purchased 6 movie
tickets for $57.30.
How much does
one movie ticket
cost?

Answers

Answer:

Each ticket costs $9.55

Step-by-step explanation:

You divide 57.30 by the number of tickets(6).  

57.30/6 = 9.55

Answer:

6 movie = $57.30

1 movie = $x

57.30 ÷ 6

=  $9.55 for one movie ticet

Step-by-step explanation:

7=100z what does z equal?

Answers

Answer:

z = 7/100

Step-by-step explanation:

Answer:

Step-by-step explanation:

7/100z

pls help it’s timed loll

Answers

Answer:

A

Step-by-step explanation:

2.2*4 = 8.8

8.8+1.7= 10.5

Answer:

The answer is A 2.2

Step-by-step explanation:

2.2×4=8.8

8.8+1.7=10.5

what does a square pluse be square

Answers

Answer:

a squared + b squared = c square

Step-by-step explanation:

In this formula c represents the length of the hypotenuse a and b are the legnths of the other two sides. if two sides of a right triangle are known you can subsitute these values in the formula to find the missing side

is y=6x+3 proportional or nonproportional

Answers

Answer:

f the x and y coordinates form proportional relationships, then there is some non-changing number (a constant) that when multiplied times x will create y

Step-by-step explanation:

Mike has $72 and he needs to buy some apples. Which of these equations would represent mike's situation of the apples cost $0.60 per apple and he wanted to find out how many apples he could buy

Answers

Answer:

120 apples

Step-by-step explanation:

Given data

Total amount= $72

Cost per apple = $0.60

The number of apples = Total amount/Cost per apple

substitute

The number of apples= 72/0.6

The number of apples= 120 apples

Hence he will buy 120 apples

Find the unknow measures of y and x.​

Answers

9514 1404 393

Answer:

  x = 2 m

  y = 30°

Step-by-step explanation:

The side lengths of ΔDEF are 3/9 = 1/3 of those of ΔABC.

  x = DF = 1/3(AB) = (1/3)(6 m)

  x = 2 m

__

Angle measures of ΔDEF are the same as those of the corresponding angles of ΔABC.

  y = ∠B = ∠E = 30°

  y = 30°

the breadth of a rectangular handkerchief is 10 cm shorter than its length .if the perimeter of the handkerchief is 100cm. find its length and breadth..
plz help me​

Answers

Step-by-step explanation:

Perimeter = 2(l+b)

2(x+x-10)=100cm

(x+x-10)= 100 divided by 2

(x+x-10)=50

2x-10=50

2x=50+10,60

x=60 divided by 2

X =30

Length = 30cm

Breadth= 30-10= 20cm

PLEASE MARK MY ANSWER AS THE BRAINILIEST!

Answer:

solution given:

length[l]=xcm(let)

breadth [b]=(x-10)cm

perimeter of rectangle [P]=100cm

we have

P=2[l+b]

100cm=2[x+x-10]

2x-10=[tex] \frac{100}{2} [/tex]

2x=50+10

x=[tex] \frac{60}{2} [/tex]

:.x=30cm

So

length[l]=x=30cm

breadth [b]=(x-10)=30-10=20cm

Pasha traveled 217 miles in 3.5 hours, how far does she travel in 1 hour

Answers

62 miles 217/3.5 to get mph then mph is 62 so every hour they travel 62 miles

4/5 cm * 3/8 cm
please answer fast ​

Answers

Answer:

= 3/10 cm or you can put 0.3 cm

what is the number sentence​

Answers

Answer:

A number sentence is a mathematical sentence made up of numbers and signs. So for example 15 + 7.

They can use any of the mathematical operations so addition, subtraction, multiplication and division

Number sentences can be true or false. Example, 5 + 7 = 13

good luck, i hope this helps :)

FInd the value of x/

Answers

Answer:

x=18

Step-by-step explanation:

The ratio of the perimeter of a square A and square B is 4:3. The side of square B is 3 m less than the side
of square A. What is the length of the side of square A?
please answer

Answers

Answer:

x = 12

Step-by-step explanation:

x = length of side of square A

'x-3' represents length of side of square B

Perimeter of square A = 4x

Perimeter of square A = 4x - 12

we can set up the following proportion based on ratio of 4:3

4x / 4 = 4x - 12 / 3

cross-multiply:

4(3x) = 4(4x-12)

12x = 16x - 48

-4x = -48

x = 12

PLSPSPSLS HELP MATHHH GRADE 5-6

Answers

median: 80
lower quartile: 65
upper quartile: 95

56 + (-56)
Find each sum

Answers

Answer:It equals 0.

Step-by-step explanation:

Because the 56 in parenthesis is a negative so when you add it equals nothing.

help me with maths :)

Answers

sin J: 5/13, 0.38
cos J: 12/13, 0.92
tan J: 5/12, 0.42

sin K: 12/13, 0.92
cos K: 5/13, 0.38
tan K: 12/5, 2.40

A small plane has 20 rows of seats. Each row has 4 seats.
help me plz!

Answers

Answer:

there are 5 sections

Step-by-step explanation:

and how you want us to help?:))

There are 2 cats to 5 dogs. Which of the following is an equivalent ratio of cats to dogs?

Answers

Answer:

See below.

Step-by-step explanation:

The ratio of cats to dogs would be 2/5. This is the simplest ratio, but I assume you are looking for other ratios that are equal to 2/5

Since you did not provide choices to pick from, I can't really answer your question. But, some ratios that are equal to 2/5 are 4/10, 6/15, 8/20, and 10/25.

Okay I don't know this one either so uh help please

Answers

9514 1404 393

Answer:

  (a)  A'(-2, 1), B'(-4, -3), C'(-7, 0)

Step-by-step explanation:

If X is the center of rotation, the coordinates of point P are transformed like this:

  P' = -(P -X) +X

  P' = 2X -P

  (x, y) ⇒ (2(-5) -x, 2(3) -y)

  (x, y) ⇒ (-10-x, 6-y)

__

Your points are transformed to ...

  A(-8, 5) ⇒ (-10-(-8), 6-5) = A'(-2, 1)

  B(-6, 9) ⇒ (-10-(-6), 6-9) = B'(-4, -3)

  C(-3, 6) ⇒ (-10-(-3), 6-6) = C'(-7, 0)

These coordinates match the first choice.

angle sum theory

PLS HELP!!

A)74°

B)92°

C)83°

D)82°

Answers

Answer:

the answer must be 74 or 82

Answer:

It's 58

Step-by-step explanation:

That's the answer

Where will Jack and Nolan meet​

Answers

I got 2.8 and 5.4 because they don’t directly meet where I graphed it.

Lee performed the best on stage because the other contestant were not as confident as (him, he)​

Answers

Answer:

him or he was

Step-by-step explanation:

Halp aspp


give brialest​

Answers

Answer:

Cant see the full photo {error}

Which point is on the graph of f(x)=2x5^x

Answers

Answer: 1, 10



Step by step explanation:

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