Ashlee is placing a rug in the middle of her bedroom. The length of the rug is two feet more than the width.

What is the area of the bedroom?

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:

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

i.e. option B is correct.

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.

To learn more on transformation click:

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Answer: -628

Step-by-step explanation:

F(140) = 212 - 6(140)

F(140) = 212 - 840

F(140) = -628

Answer:

M1=136

m4=180-136

=44////

Answer:

12 passengers so four more can travel in the bus.

Step-by-step explanation:

384/8= rs 48 per person.

amount= 576

576/48 = 12 passengers.

Step-by-step explanation:

here

8 passengers=Rs. 384

1 passenger= Rs. 384/8

=Rs. 48

Rs. 576= ? passengers

now,

Rs. 576/ 48

= 12passengers

12 passengers - 8 passengers

= 4 passengers

therefore, 4 more passengers can travel in the bus fare amount to Rs. 576.

Answer:

I don't know.

Step-by-step explanation:

I don't know.

Answer: 32 meters

Step-by-step explanation:

Answer: I guess High School is as bad as my big sister says it is.

Step-by-step explanation:

I'm in 8th grade, I'm going to highschool this yearrrr! Poor me...

Answer:

15 and 12 makes a pattern of -3

25 and 20 makes a pattern of -5

35 and 28 makes a pattern of -7

Step-by-step explanation:

5 x 3=15

5 x 5=25

5 x 7=35

Answer:14

Step-by-step explanation:

Answer:

44°

Step-by-step explanation:

This is an inscribed angle and its measure is equal to the measure of arc it sees (minor arc BC in this case)

88 ÷ 2 = 44°

Answer:

False, true, false, true

Step-by-step explanation:

Sin T = 7/25

Cos T = 24/25

Sin C = 24/25

Cos C = 7/25

Answer:

750

Step-by-step explanation:

Answer:

She had $455 before

Answer:

$41686.65

Step-by-step explanation:

Given data

Principal = $92,637

Rate= 9%

Time= 5 years

The simple interest expression is given as

SI= PRT/100

Substitute

SI= 92637*9*5/100

SI= 4168665/100

SI=$41686.65

Hence the interest is $41686.65

Answer:

3000=3000*0.02t

3000/60=t

t=50 yrs

Step-by-step explanation:

Answer:

14.5

Step-by-step explanation:

2x=7*5-6 will be 14.5

Answer:

One solution.

Step-by-step explanation:

Since the right side of the equation is a constant, there can only be one solution:

[tex]2x+6=7*5[/tex]

[tex]2x+6=35[/tex]

[tex]2x=35-6[/tex]

[tex]2x=29[/tex]

[tex]x=14.5[/tex]

14.5 is the only answer.

Answer:

the answer is 9^8

Step-by-step explanation:

9^3 * 9^5 = 9^ 3 + 5 = 9^8

Answer:

1 . 6 , 2 is 18 ,6

2.4,5 is 12 ,15

3. 9,4 is 27,12

but is ans is wrong

Answer:

x-17

Step-by-step explanation:

Answer:

x-17

I might be incappable

Answer:

408.7 in^2

Step-by-step explanation:

If you want to know how to find the area of a regular octagon by hand, the easiest procedure is to apply the standard formula for the area of a regular polygon. The formula is the following:

area of regular polygon = perimeter * apothem / 2,

where the apothem is the distance for the center of the polygon to the mid-point of a side. The perimeter can be calculated a few ways: by summing up the length of each side, multiplying the length of one side by the number of sides.

Answer:

A = 3.14

Step-by-step explanation:

A = π[tex]r^{2}[/tex]

A = 3.14 x [tex]1^{2}[/tex]

(diameter = 2)

(remember, radius is half of the diameter)

(radius = 1)

A = 3.14

Answer:

3x+4

Step-by-step explanation:

The algebraic expression will be :  3x + 4

An expression built up from integer constants , variables and algebraic operations .

Let the number be : x

now , in the algebraic expression for 4 more then 3 times a number

First we need to make the number 3 time  = 3x

then in that expression we need to add 4 , we get = 3x+ 4

The algebraic expression will be :  3x + 4

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Answer:

your answer will be y= -1/6x+(-1)

Step-by-step explanation:

I hope this helps ^_^