6
AXYZ will be translated so that the coordinates of X' are (5,11).
y
Y
14
13
12
X
11
10
9
8
N
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
What will be the coordinates of Z' ?
(5,8)
B (6,7)
© (7,6)
D (8,5)

Answers

Answer 1

Answer:

Isometry: An isometry is a transformation that maintains congruency.  This means that the transformation does not change the figure's size or shape.

Make sure your child is familiar with the Cartesian coordinate system including the horizontal x-axis, the vertical y-axis, and the (x,y) convention used for locating points.

If you have not already done so, you may wish to review this congruency lesson with your child.

Translations

This section will help your child to translate congruent figures on a Cartesian plane. It will also introduce translation vectors which show the distance and direction of the translation.

Translations

Figure J is the pre-image. Figure S is translated.

A figure is a translation if it is moved without rotation.

Translation Vector

A Translation Vector is a vector that gives the length and direction of a particular translation. Vectors in the Cartesian plane can be written (x,y) which means a translation of x units horizontally and y units vertically.

figure being translated

Vectors translations can be written as shown in either of these two ways:

format example for writing vectors

This vector can be said to be ray AB or vector D.

You translate a figure according to the numbers indicated by the vector.  So if one point on a figure has coordinates of (-3,3)  and the translation vector is (-1,3), the new coordinate is (-4,6). You add or subtract according to the signs in the numbers in the vector.

Work through the two examples below with your child to see how to apply translation vectors.

square translated on cartesian grid

The red square's coordinates are:

(-4,3); (-4,8); (-9,3); (-9,8).

What are the coordinate pairs under a translation vector of (1,-1) as shown by the blue square?

The new coordinates are:

(-3,2); (-3,7); (-8,2); (-8,7).

You can see that the translation did not move the figure far because the vector translation is small.

square translated on cartesian grid

We will try a different vector translation of (3,-9) on the same red square

The new coordinates are:

(-1,-6); (-1,-1); (-6,-6); (-6,-1).

Get you child to try the next example. Do not look at the answer until he or she has tried to work it through the task.

single triangle on cartesian grid

Task: Translate ΔABC with a vector translation of (6,-2)

Steps:

Find the coordinates of Δ ABC.

Add 6 to the X coordinates and subtract 2 (or add -2) from the Y coordinates.

Plot the new coordinates on the grid.

Answer and Explanation

Coordinates of ΔABC are:

(-5,1); (-2.5,7); (0,1)

Add 6 and subtract 2

A1 = (-5 + 6, 1 - 2) = (1,-1)

B1 = (-2.5 + 6, 7 - 2) = (3.5,5)

C1 = (0 + 6, 1 - 2) = (6,-1)

Plot ΔA1B1C1

Rotations

This section will show your child how to rotate a figure about the origin on a Cartesian plane. Work through the two examples below:

Note: Make sure your child knows that the origin is the intersection of the X and Y axes; (0,0) on the Cartesian plane.

Rotation Transformation: Example 1

Look at the four triangles on the Cartesian plane below. Each one is rotated about the origin as shown in the table.

Triangle B Triangle C Triangle D

90° rotation of Triangle A about the origin 90° rotation of Triangle B about the origin 90° rotation of Triangle C about the origin

 180° rotation of Triangle A about the origin 180° rotation of Triangle B about the origin

   270° rotation of Triangle A about the origin

The coordinates are:

Triangle A (-2,2) (-10,2) (-6,8)

Triangle B (2,2) (2,10) (8,6)

Triangle C (2,-2) (10,-2) (6,-8)

Triangle D (-2,-2) (-2,-10) (-8,-6)

Note the pattern in the coordinates for corresponding vertices on the triangles.

Rotation Transformation: Example 2

The coordinates of Pentagon ABCDE are:

(0,4); (7,4); (9,2); (7,0); (0,0)

Pentagon ABCDE is rotated 180° about

the origin making the coordinates of

Pentagon A1B1C1D1E1:

(0,-4); (-7,-4); (-9,-2); (-7,0); (0,0)

Note how the coordinates of

corresponding vertices are opposite

integers (just the +/- sign is different).

This is always the case with 180°

rotations about the origin.

Reflections

This section will help your child to reflect a figure over an axis on a Cartesian plane

Work through the two reflection examples below.

Reflection Transformation: Example 1

The coordinates of LMNO are:

(-7,5); (0,5); (-2,1); (-5,1)

LMNO is reflected over the X-axis

making the coordinates of

L1M1N1O1:

(-7,-5); (0,-5); (-2,-1); (-5,-1)

Note how the x-coordinates remain the

same but the y-coordinates change to

their opposite integer (i.e. the sign changes).

This is always the case with reflections over the X-axis.

Step-by-step explanation:

Answer 2

The solution is, the coordinates of Z'  will be z' = (6,7),

i.e. option B is correct.

What is transformation?

A transformation is a dramatic change in form or appearance. An important event like getting your driver's license, going to college, or getting married can cause a transformation in your life. A transformation is an extreme, radical change.

here, we have,

Given that,

X' are (5,11).

now, See attachment

Required that,

The image of Z i.e. z'

From the attachment:

X =(7,11)

This implies that:

X' = ( x- 2, y)

Using the same rule for z;

z=(8,7)

z' = (8-2, 7)

z' = (6,7)

Hence, The solution is, the coordinates of Z'  will be z' = (6,7),

i.e. option B is correct.

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6AXYZ Will Be Translated So That The Coordinates Of X' Are (5,11).yY141312X111098N76543210 1 2 3 4 5

Related Questions

write an equation of a line that passes through (1,1)and (6,6)

Answers

Answer:

y=x

Step-by-step explanation:

When y=x, then the line goes up 1 and right 1.

Here are the
the first 5 terms of a sequence.
29 25 21 17 13
Find an expression, in terms of n, for the nth term
of this sequence.

Answers

Step-by-step explanation:

hope it help you.......

Expand "6y" in algebra​

Answers

Answer:

6 x y

Step-by-step explanation:

Expanded

Or add y 6 times

y + y + y + y + y + y

Answer:

Step-by-step explanation:

y + y + y + y  + y + y

Hope that helps!

How the heck do I do this

Answers

Total surface area of a cylinder=2pi(radius)(height)+2pi(radius)square

Either enter an exact answer in terms of T or use 3.14 for 7 and enter your answer as a decimal.
d=2

Answers

Answer:

N CCX  XN

Step-by-step explanation:

Last season, Mya made 78% of her goal shots. Chad made 4/5 of his goal shots. Who has the better average?

Answers

Chad did 4/5 as a percent is 80% so 80% is larger than 78% so the answer is Chad did the better average
Chad has the better average because 4/5 is 80% and 80%>>>>78%

You sell small and large candles at a craft fair. Small candles cost $4 each and large candles cost $6 each. You collect $144 after selling a total of 28 candles. How many of each type of candle did you sell? Write a linear system to represent the situation. Be sure to define your variables.

Answers

Answer: Small Candle = 12, Large Candle = 16

Step-by-step explanation:

Equation is this, s+l=28 2nd equation is 4s+6l=144

now you multiply every number in the second equation by -6 since positive 6 is the second equations second constant. Now you got -6s-6l=-168 And 4s+6l=144. The -6l and positive cancel so now you got -6s + 4s = -168+144. Now you got -2s = -24. Divide them both by negative two then you get s = 12. 28 candles total - 12 = 16 so 16 large candles and 12 small. L = large candles, S = small candles.

Answer:

8 small candles

16 large candles

Step-by-step explanation:

1. Approach

Set up a system of equations to solve this problem. Call the number of small candles sold (x), and the number of large candles sold (y). Have one expression model the amount of money earned, the other model the number of candles sold. Then, solve this system of equations using the process of elimination. In the process of elimination, one multiplies one of the equations by a term such that one of the coefficients of a variable in one of the equations is the additive inverse of the corresponding variable in the other equation. This means that when one adds the two equations, one of the variables will eliminate. Then one can solve for the other variable, and finally, substitute the value of the variable that one found back into one of the equations, and solve for the value of the other variable.

2. Set up a system of equations

Use the given information to set up a system of equations to describe the amount earned, and the amount sold

x + y = 28 -> amount sold

4x + 6y = 144 -> amount earned

3. Solve the system

As explained above, the process of elimination is a method of solving a system of equations. In the process of elimination, one multiplies one of the equations by a term such that one of the coefficients of a variable in one of the equations is the additive inverse of the corresponding variable in the other equation. This means that when one adds the two equations, one of the variables will eliminate.

x + y = 28 (*-4)

4x + 6y = 144

-4x - 4y = -112

4x + 6y = 144

___________

2y = 32

/2     /2

y = 16

4. Solve to find out how much of the other candle was sold

Now back solve, substitute the found value into one of the equations, and solve to find the other value

x + y = 28

y = 16

x + 16 = 28

    -16     -16

x = 8

subtract 12a² + 15ab - 20b² from 15a² + 10ab + 8b²

help.​

Answers

Answer:

3a^2 + 28b^2 - 5ab

Step-by-step explanation:

here's your solution

=> to subtract (12x^2 + 15ab - 29b^2) from

( 15a^2 + 10ab + 8b^2)

=> (15a^2 + 10ab + 8b^2) - (12a^2 + 15ab - 20b^2)

=> 15a^2 + 10ab + 8b^2 - 12a^2 - 15ab + 20b^2

=> 15a^2 - 12a^2 + 8b^2 + 20b^2 + 10ab - 15ab

=> 3a^2 + 28b^2 - 5ab

hope it helps

Can someone help me out with this question as I’m completely stuck

Answers

Answer:

Step-by-step explanation:

∠BEF = ∠ABE   {Alternate interior angle}

∠BEF = 60

∠EQR = ∠ BEF         {Corresponding angles}

∠EQR = 60

In ΔEQR

∠QER + ∠EQR + ∠ERQ = 180 {angle sum property}

80 + 60 +x = 180

140 + x = 180

          x = 180- 140

x = 40

Please help look and photo

Answers

Answer:

.

Step-by-step explanation:

Depending on traffic, Danielle’s drive to the park is p minutes from work and 90 minutes from the park to her home. If Danielle’s total commute (c) took two hours today, how long was Danielle’s drive to the park from work? Set up your equation when total commute time (c) depends on the time to drive to the park (p).

Equation: ______________
p=88 minutes
p=70 minutes
p=40 minutes
p=30 minutes

Answers

Answer:

The equation is;

p + 90 = 120 minutes

Danielle’s drive from work to the park took 30 minutes ( p = 30 minutes)

Step-by-step explanation:

Here, we want to write and solve an equation

Here, we want to get the time taken by Daniele from the park to work

From the question, the total commute is two hours

since 1 hour is 60 minutes, it follows that 2 hours is 120 minutes

Now, if we added the time taken to commute both journeys, we have the total as 2 hours

This means;

p + 90 = 120 minutes

p = 120 - 90

p = 30 minutes

The same amount deposited weekly into a bank account can be represented by a
A: Linear
B: Exponential
C: Quadratic

Answers

Answer:

I think B

Step-by-step explanation:

aaaaAjshfbd pub d guy x gu dc

The same amount deposited weekly into a bank account can be represented by a Linear.

Therefore, option A is correct.

What is Linear Function?

Linear functions have a straight line as their graph. The following is the form of a linear function. a + bx = y = f(x). There is one independent variable and one dependent variable in a linear function. x is the independent variable, and y is the dependent variable.

The degree of the model for data presented as ordered pairs can be determined by determining the differences between dependent values.

The model will be linear if the initial difference is the same value.If the second difference has the same value as the first, the model is quadratic.If the number of times the difference is calculated before obtaining repeated values surpasses five, the model could be exponential or another unique equation.

If the same amount deposited weekly into a bank then the difference between consecutive deposits will be same.

Thus, the situation shows the linear function.

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Need help quick Picture provided

Answers

C^2=a^2+b^2
C^2=20^2+15^2
C^2=400+225
C^2=X+10
(X+10)^2=625
X+10= √625
X+10=25
X=25-10
X=15

C^2=a^2+b^2
C^2=15
15^2=a^2+b^2
225=9^2+b^2
b^2=225-81
b^2=144
b= √144
b=12
b=y
y=12

Help! If u get it i will mark brainliest!
Triangle QRS is a right triangle. mR = 34° What is mQ? A. 34°, B. 46°, C. 56° D. 66°

Answers

Answer:

c

Step-by-step explanation:

i just did it

please help i will mark brainliest.

Answers

Answer:

d answer is correct

Step-by-step explanation:

I hope it will help you

The answer should be D because, you see the little addition plus signs by the circles, and they are adding every 5 circle and you have 8 in all in each circle.

So, 5 circles 5 shaded triangles and eight triangles in all.

Hope this helps, but if I get this wrong m sorry.

In the diagram below, AC intersects ABDE at B. Choose True or False for each statement

Answers

Answer:

false, true . false

Step-by-step explanation:

if u want an explanantion you can ask me :)

Answer: a. True b. True c. False

Explanation:

a. 65+25 =90 complementary angles add up to 90°

b. 65 + b + 25 = 180

90 + b = 180

b = 180 - 90

b = 90

Check-

65 + 25 + 90 = 180

90 + 90 = 180

180 = 180 ✅

c.not vertical angles because they aren’t across from eachother

please help me find the area of the composite figure :)

Answers

Find the area of both shapes in the composite figure and add them together.

A of rectangle is 6 x 12
= 72

A of triangle is 1/2 x 8 x 5
=20

Add them together to get 92 inches^2

Hope this helps!!

I need help ASAP!! can u do this? :)

Answers

The answer is 48 because you have to do is 21 x 4 which is 48
It’s 48...............

Find the geometric mean between 28 and 32. Round to the nearest tenth if necessary.

Answers

Answer: The geometric mean is √24 * 32 = √768 = 16√3.

The geometric mean between 28 and 32 is 28.29 after using the formula of the geometric mean.

What is mean?

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

Let x be the geometric mean between 28 and 32

The formula for the geometric mean:

x = √(a×b)

x = √(28×32)

x = √800

x = 20√2

x = 28.284

or

x = 28.29

Thus, the geometric mean between 28 and 32 is 28.29 after using the formula of the geometric mean.

Learn more about the mean here:

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Find the value of x for brainliest

Answers

Answer:

∅=53°

Step-by-step explanation:

Given opposite and hypothenuse. Use the sin ratio:

sin∅=opp/hyp

sin∅=12/15

∅=sin-1 12/15

∅=sin-1 0.8

∅=53.13010235415.

∅=53°

The table shows a relationship between values of x and y.

X. 2 3 4 6
Y. 7 17 31 49

Which of the following equations describes the relationship in the table? A. Y = 10x - 3
B. y = x2 + 3
C. y= 2x2 + 1
D. y=2x² - 1​

Answers

Answer:

The answer is D.

Step-by-step explanation:

For each of these questions, you just have to substitute one of the x values, where the X is in the equation. Then the equation is true is the Y value you solve for is the same as the corresponding  Y value.

Write the ratio in its simplest form using words. 14 cups to 28 cups

Answers

the ratio is 1:2 in simple form because 28/2 is 14.

The black triangles are similar. Identify the type of segment shown in blue and find the value of the variable. altitude base hypotenuse median Question 2 y=

Answers

Answer:

Hello your question is incomplete attached below is the complete question

answer : ALTITUDE , x = 24

Step-by-step explanation:

The type of segment shown in Blue is ALTITUDE segment

This is because

Angle BCD = Angle CEG (opposite angles)

Angle ACD= Angle CFG (opposite  angles)

Angle ADC = Angle BCD= Angle CEG = Angle CFG

It can be seen that the triangles are similar hence

 18/27=16/x

therefore  X  =24

The perimeter of a rectangular window is 242 cm.
If the length of the window is 66 cm, what is its width?
Width of the window: 0
cm

Answers

Answer:

The width of the window is 176 cm

Step-by-step explanation:

The perimeter is the outside of a shape. If the perimeter is 242 cm and we know the length is 66 cm, we use what we have. We take 242 and subtract it by 66 and get 176 cm

(-2,19)(10,-11) find the slope

Answers

Answer:

-5/2

Step-by-step explanation:

Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\[/tex]

         [tex]= \frac{-11-19}{10-[-2]}\\\\=\frac{-30}{10+2}\\\\=\frac{-30}{12}\\\\=\frac{-5}{2}[/tex]

The probability that it rains is about 20%.
The probability that the bus is late is about 8%.
The probability that it rains and the bus is late is about 3%.
The probability that the train is late is about 5%.
The probability that it rains and the train is late is about 1%.

what can you conclude about the rain and the students commute on the bus and train?​

Answers

Let A= probability it rains
P(A)=0.2
Let B be the probability that the train is late = 0.05
P(B)=0.05
A and B is A∩B= the probability it rains and the bus is late =0.01
probability pf (A and B)=0.01
7) independent events are related by expression:
A∩B=P(A)*P(B)
=0.2*0.05=0.01
check :
p(A|B)=P(A∩B)÷P(B)=0.01/0.05= 0.2
the two event are independent

Use long division to divide 12x3 - 11x² + 9x + 16 by
4x + 3

Answers

Answer:

THE ANSWER IS 3×2-5×+6

Step-by-step explanation:

HERE IS A PIC OF THE WORK

the cost of a pair vans is 58.65 you have a 40% off coupon how much is 40% off coupon

Answers

Answer:

$23.46 off

Step-by-step explanation:

final price: $35.19

Answer:23.46

Step-by-step explanation:

58.65 divided by 0.40 which is equivalent to 40%

4 pairs of shoes cost $80. What is the cost 7 pairs of shoes ?

Answers

Answer:

7 pairs = 140

Step-by-step explanation:

7 pairs of shoes will cost $560

explanation: 80 x 7 is 560

4x=-x+10
I’m confused?

Answers

Answer:

x=2

Step-by-step explanation:

4x=-x+10

To find x, we first add x to each side to get rid of -x on the right side.

5x=10

Then, we divide each side by 5 to get x by itself.

x=2

And that's your answer :)

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