Ava wants to draw a parallelogram on the coordinate plane. She
plots these 3 points.

Part A
Find and label the coordinates of the fourth vertex, K, of the
parallelogram. Draw the parallelogram.

Part B
What is the length of side JK? How do you know?​

Answers

Answer 1

Answer:

[tex]k =(2,1)[/tex]

[tex]JK = 2[/tex]

Step-by-step explanation:

Given

[tex]J = (0,1)[/tex] ---- [tex](x_1,y_1)[/tex]

[tex]H = (1,-2)[/tex] --- [tex](x_2,y_2)[/tex]

[tex]I = (3,-2)[/tex] --- [tex](x_3,y_3)[/tex]

See attachment for grid

Solving (a): The coordinates of K

The parallelogram has the following diagonals: IJ and HK

Diagonals bisect one another. So:

Midpoint of IJ = Midpoint of HK

This gives:

[tex]\frac{1}{2}(I + J) = \frac{1}{2}(H+K)[/tex]

[tex]\frac{1}{2}(x_3+x_1,y_3+y_1) = \frac{1}{2}(x_2+x,y_2+y)[/tex]

[tex]\frac{1}{2}(3+0,-2+1) = \frac{1}{2}(1+x,-2+y)[/tex]

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

Multiply through by 2

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

By comparison:

[tex]1 + x = 3[/tex]

[tex]-2 + y = -1[/tex]

Solve for x and y

[tex]x = 3 - 1 =2[/tex]

[tex]y = -1 +2 = 1[/tex]

So, the coordinates of k is:

[tex]k =(2,1)[/tex]

The length of JK is calculated using distance (d) formula

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

[tex]J = (0,1)[/tex] ---- [tex](x_1,y_1)[/tex]

[tex]k =(2,1)[/tex] ---- [tex](x_2,y_2)[/tex]

So:

[tex]d = \sqrt{(0 - 2)^2 + (1 - 1)^2[/tex]

[tex]d = \sqrt{(- 2)^2 + (0)^2[/tex]

[tex]d = \sqrt{4 + 0[/tex]

[tex]d = \sqrt{4[/tex]

[tex]d = 2[/tex]

Hence:

[tex]JK = 2[/tex]

Ava Wants To Draw A Parallelogram On The Coordinate Plane. Sheplots These 3 Points. Part AFind And Label

Related Questions

Helppppppppppppppppp

Answers

Answer:

I just need points sorry love But the answer is A.

Step-by-step explanation:

Four fifths of the 35 kittens finish their milk how many did not finish their

Answers

Answer:

7 kittens did not finish their milk

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

lets find the answer

Answers

Answer:

(-3,0)

Step-by-step explanation:

1) find the coordinate of x

x = -3

2) find the coordinate of y

the point lies on x axis so y = 0

The coordinates are (-3, 0)

:)

what is the product of (3Y^-4) (2Y^-4)

Answers

Answer:

the product is 6/Y^8

Step-by-step explanation:

10 Students were surveyed.
How many hours do you study a week?
8 2 2 6 14 10 3 5 4
Determine the following:
A) Mean
B) Mode
C) Median
Show work please
Will mark brainlisted

Answers

Answer:mode

Step-by-step explanation:5+4+9+9+3+75+1=mode

The graph of a polynomial function may have no x-intercepts.

true or false

Answers

true (I don't know if this is the answer but it would be my guess)

You notice that another cupboard door is in the shape of a square that is divided into two isosceles triangles. You measure the height of the cupboard to be 16 inches. What is the area of one of the triangles shown on the face of the cupboard door? Show your work. ​

Answers

Answer:

i wrote "13 8/9 because 16 2/3 x 16 2/3= 50/3 x 50/3 = 250/9 then 250/9 ÷ 2 = 125/9 = 13 8/9"

Step-by-step explanation: if u add in some words or something so you teacher isnt sus hope you pass!!

A lidless box is constructed by cutting a square with side length x from a rectangular sheet of paper with dimensions a x b. After the cut is removed, the sides are folded up to form the
box.
a) Find the value of x (in terms of a and b) that maximizes the volume of the box.
b) Find the value of x that maximizes the volume of the box when a = 8.5 inches and b= 11 inches.

Answers

Answer:

a) [tex]x =\dfrac{a+b -\sqrt{(a + b)^2 - 3\cdot a \cdot b} }{6}[/tex]

b) The volume of the box is maximized when 'x' is approximately 1.585 feet

Step-by-step explanation:

a) Let 'a' represent the length of the rectangular sheet of paper and let 'b' represent the with of the rectangular sheet of paper, we have;

The length of the side of the square cut from the corners of the rectangular sheet of paper = x

The length of the box formed after cutting the square sides are;

The length of the box, l = a - 2·x

The width of the box, w =  b - 2·x

The height of the box, h = x

The volume of the box, V = l × w × h = (a - 2·x)·(b - 2·x)·x = 4·x³ - 2·a·x² - 2·b·x² + a·b·x

The value of 'x' that gives the maximum volume of the box is given by finding the extremum of the volume, 'V', of the box as follows;

At the extremum, dV/dx = 0

∴ d(4·x³ - 2·a·x² - 2·b·x² + a·b·x)/dx = 12·x² - 4·a·x - 4·b·x + a·b = 0

12·x² - 4·(a + b)·x + a·b = 0

[tex]x = \dfrac{4\cdot (a + b) \pm \sqrt{(-4\cdot (a + b) )^2-4 \times12\times a \cdot b } }{2 \times 24} =\dfrac{a+b\pm\sqrt{(a + b)^2 - 3\cdot a \cdot b} }{6}[/tex]

Found from part (b), the value of 'x' (in terms of 'a' and 'b') that maximizes the volume of the box is [tex]x =\dfrac{a+b -\sqrt{(a + b)^2 - 3\cdot a \cdot b} }{6}[/tex]

b), When a = 8.5 inches and b = 11 inches, we have;

x = (8.5 + 11 +√((8.5 + 11)² - 3×8.5×11))/6 = 4.914

x = (8.5 + 11 -√((8.5 + 11)² - 3×8.5×11))/6 ≈ 1.585

We get;

When x = 1.585, V = 4·1.585³ - 2·8.5·1.585² - 2·11·1.585² + 8.5·11·1.585 ≈ 66.15

When x = 4.914, V = 4·4.914³ - 2·8.5·4.914² - 2·11·4.914² + 8.5·11·4.914 ≈ -7.65

Therefore, the value of 'x' that gives the maximum volume of the box is x = (8.5 + 11 -√((8.5 + 11)² - 3×8.5×11))/6 ≈ 1.585

(The value of 'x' in terms of 'a' and 'b' is therefore;

[tex]x =\dfrac{a+b -\sqrt{(a + b)^2 - 3\cdot a \cdot b} }{6}[/tex])

The volume of the box is maximized when, x ≈ 1.585 feet

7
Which equation can be used to describe the relationship between x and y shown in the graph
below?
3x + 2
D-3x - 6
D
3-6
D3X2

Answers

C: y=3x-6, it’s based on the 3:1 slope and -6 y-intercept
See where the end point starts

2x + 2y = -2
3x - 2y = 12
Answer:

Answers

Answer:

(2,-3)

Step-by-step explanation:

2x + 2y = -2

3x - 2y = 12

Add the two equations to eliminate y

2x + 2y = -2

3x - 2y = 12

-----------------------

5x   = 10

5x/5 = 10/5

x = 2

Now find y

2x+2y = -2

2(2)+2y = -2

4+2y = -2

Subtract 4 from each side

4-4 +2y = -2-4

2y = -6

Divide by 2

2y/2 = -6/2

y = -3

(2,-3)

Is x=2 a solution to the equation below?
4(x-1)-3(x-2)=-8

Answers

Answer:

No

Step-by-step explanation:

To find out if 2 is a solution, replace all the x's with 2.

4(2 - 1) - 3(2 - 2) =8

4(1) - 3(0) = 8

4 - 0 = 8

4 = 8

Nope!  False!  2 is not a solution.

The cost (c) for g number of gelato ice cream is shown in the table. Complete the table and graph the proportional relationship between the number of gelatos purchased and the total cost.

g c
2 8
5
6
8

Answers

Answers below:
5 20
6 24
8 32

What is the mean absolute deviation of the data set?

{5, 7, 12, 11, 3, 10}

Answers

Answer:

3

Step-by-step explanation: First, you find the mean of the data set. Then you take that mean and find the difference of that and each value, you add those up and find the mean of that number.

4. M is the midpoint of XY. If XM = 8-t and MY = 5t-10, find tand XY.​

Answers

Answer:

XY = 10

Step-by-step explanation:

By the definition of midpoint, XM would be equal to MY, so we can set both equations equal to each other;

XM = MY

8 - t = 5t - 10

=> Now add "t" to both sides of "="

8 = 6t - 10

=> add 10 from each side;

18 = 6t

=> Finally divide 6 on each side

3 = t

Now that we have the value for t, we can substitute 3 in place of "t" in any of the equation above and solve, when we have the answer, multiply it by 2 to get the value for XY.

=> 8 - 3

=> 5

=> XY = 5 * 2

=> XY = 10

Hope this helps!

help me out please real answers only (20 points)

Answers

Answer:

hope this will help

if correct please give brainliest

a man cycles a distance of 63km in less than 3hours what is the average speed​

Answers

Answer:

21 km/h

Step-by-step explanation:

PLEASE HELP ASAP!!!

Answers

Answer:

4. x=0 x=5

5. x=-4 x=8

A person is wearing a bracelet with 11 settings around the bracelet. How many different ways can 12 birthstones be

arranged around the bracelet?

O 10!

11!

O 12!

Answers

Answer:

10

Step-by-step explanation:

I think I hope this helps

You and three of your friends go parasailing for 128.40 you split the cost
evenly. How much does each person pay?

Answers

Answer:

40 each i think maybe 30 if not

U have $77 in your bank account than you write a check for $100 at the store how many do I have now? Please show work

Answers

Answer:

$-23

77 - 100 = -23

Help please!!
and Thank you!!
Find the surface area.

Answers

Answer:

2411.52 mm²

Step-by-step explanation:

[tex]40^{2} =32^2+d^2[/tex]

→ [tex]d^2= 1600-1024[/tex]

→[tex]= 576[/tex]

→ [tex]d= 24[/tex]      [tex]so, (radius=12[/tex]

[tex]Total~ surface ~ area= (2\pi r)*height[/tex]

→ [tex](2*3.14*12*82)[/tex]

[tex]= 2411.52 mm^2[/tex]

-------------------------------

hope it helps...

have a great day!!

Answer:

2411.52 mm²

Step-by-step explanation:

hope its helpful

Help me with this please.

Answers

sorry I don’t know this one is there anyway I can help with something else
I can’t really the picture

Please answer correctly! I will mark you as Brainliest! Please No links or any joking around or I will call and report you!

Answers

answer:
(0, -3)

step-by-step explanation:
if you flip it over the x-axis it would be (0, -3) because the 3 is the y-intercept it would just be -3

Answer:

0, -3

Step-by-step explanation:

So remember, when they say reflect over the x intercept, they do not mean to reflect the x value, they mean to reflect over the hirzontal line of the graph.(x axis)

This is the same with reflection over the y intrecept. This doesnt mean y is flipped, this means that whatever point or line you have is reflected over the vertical line on the graph(y axis)

So our orginal value is (0, 3). We need to reflect over the x axis, which means that y will now be -3, since that is the opposite of what we can see when we flip the x axis.

The 0 x, of course, stays the same since its 0.

So your answer is (0, -3)

Hope this helps! :)

solve the system by substitution
5x+y=-14
5x- 3y=2

Answers

Answer:

x=-2 and y=-24

Step-by-step explanation:

plug in the value of y (-5x-14) into the second equation

what is the measure of each angle

Answers

Your answer is X=22
Step-by-step
5X - 31= 79
5x= 79+31
X=110/5
So x=22 same as on

Below. What is m∠1?

m∠1 =

Answers

Answer:

m∠1 = 70°

Step-by-step explanation:

Step 1

Sum of angles on a straight line = 180°

Hence:

180° - 101°

= 79°

Sum of interior angles in a triangle = 180°

Hence

m∠1 = 180° - (79 ° + 31°)

m∠1 = 70°

in a class of 25 students, 18 were math majors, 12 were computer science majors, and 7 were dual majors in math and computer science.
A)How many students were majoring in math only?
B)How many students were not majoring in computer science?
C) how many students were not math or computer science majors?

Answers

Answer:

Use n(u) formula of chapter sets

Step-by-step explanation:

Have a good day

11 students were majoring in math only; 13 students were not majoring in computer science; and 2 students were not math or computer science majors.

Given that in a class of 25 students, 18 were math majors, 12 were computer science majors, and 7 were dual majors in math and computer science, to determine A) how many students were majoring in math only; B) how many students were not majoring in computer science; and C) how many students were not math or computer science majors; the following calculation must be performed:

Math majors only = 18 - 7 = 11 Not majoring in computer science = 25 - 12 = 13 Not math or computer science majors = 25 - 7 - 11 - (12 - 7) = 18 - 11 - 5 = 2

Therefore, 11 students were majoring in math only; 13 students were not majoring in computer science; and 2 students were not math or computer science majors.

Learn more in https://brainly.com/question/20293703

please help me



i’m so stuck

Answers

Answer:

2 cm

Step-by-step explanation:

V=πr2h = 20π

-π                -π

r2h = 20

h= 5

r2(5) = 20

/5         /5

r2=4

/2  /2

r=2cm

(my work is complicated, but trust me 2 cm is the answer)  

A line passes through the origin and the point (3.5). What is the slope of the line? 0
3/5
-3/5
5/3​

Answers

Answer:

5/3 is the slope of the line.

Triangle DEF is shown on the coordinate grid below triangle DEF is reflected across the Y axis which role best describes this transformation

Answers

Answer:

I can’t see the picture

Step-by-step explanation:

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