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The equation for finding a new point is

[ Old Point  - Dilation Center ] * Scale Factor +   Dilation Center

However....since the origin is the Dilation Center, this simplifies to

[Old Point] * Scale Factor....so we have

(12,12) * 14  =  (168,168)

(12,4) * 14 = (168, 56)

(8,0)*14  =   (112, 0)

(5,8) *14  = (70, 112)

Here's a pic :

Multiplication Property of Equality

Addition Property of Equality

Division Property of Equality

∠A≅∠B∠B≅∠C

angle congruence postulate

transitive property of equality

angle congruence postulate

x  =  -2

To see this......imagine that we rotate [ "spin" ] the trapezoid about this line......it maps the trapezoid back to its original image

(-2, -1)   ,  (-6, -2)  ,  (-5, -5)

  A                 B              C

(2, 1)  ,    (6, 2)   ,  (5, 5)

  A'             B'            C'

Here's the pic :

Here it is https://static.k12.com/nextgen_media/assets/8080857-NG_GMT_SemA_IT_01_30.png

Simplify

Addition Property of Equality

Division Property of Equality

Symmetric Property of Equality

If you have a URL for the pic, you can just include it in the post.....we will be able to access it

If not....

1st.....you must have the image saved on your hard drive....I use the Snipping Tool  for this

2nd......click on the "Image" icon above

3rd....hit the "upload tab"

4th....choose the file you wish to upload.....hit  "open"

5th.....hit the "upload" tab......you might be asked to verify  some  "Captcha" images

An angle measures 90º if and only if the angle is right

The argument is valid by the Law of Detachment

All are expansions....the absolute value of each is  >  1

A contraction  will occur  when the absolute value of the scale factor  is  greater than 0 but less than 1

Don't see anything shown.....but....

In an isosceles triangle, two of the angles are congruent.

Rotating 90°  clockwise about the origin produces the points

(1, -3)  , ( 4, - 6)  and (1, - 6)

Reflecting these across the y axis produces

(-1, - 3) , ( -4, - 6)   and  (-1, -6)

   A'               B'                   C'

Post your problems.....we'll see what we can do.....

check again

LOL! I just tried re-uploading it...seemed to work! 

It has suddenly reappeared......ghosts in the machine....maybe????

Yep......blocked for me as well.......odd  !!!

Thanks CPhill!! That is weird...is the picture blocked for you? I don't think it was blocked last night!

Nice, hectictar.....!!!

If   3 -  ⁴√2 i    is a root, then so is the conjugate   3 +  ⁴√2 i

Let  the polynomial we are looking for be P(x)

And  suppose that P(x)  can be written as  Q(x) * R(x)

So ....let Q(x) be  formed by

( x -  ( 3 - ⁴√2 i) )  ( x -  (3  + ⁴√2 i) )   =

[ ( (x - 3) +  ⁴√2 i  ]    [  (x - 3)  -  ⁴√2 i  ]   =

(x - 3)²   +  √2

And it's clear that we will have a polynomial with rational coefficients if  R(x)  is

(x - 3)²   - √2

So

      Q(x)            *         R(x)        

[( x - 3)²  + √2 ] *  [( x - 3)²  - √2 ]    produces

(x - 3)⁴   -  2    =

x^4  -  4* x³ * 3  + 6x² * 3²  -  4x * 3³  + 3⁴  -  2   =

x^4  -  12x^3  + 54x^2  - 108x  +  79   =  P(x)

Let C1  be  the constant in Eric's polynomial  and C2  be the constant in Charles's polynomial

And we have that

[16 - 4C1] / [16 - 4C2]  =  C2 /C1     cross-multiply

16C1   -  4C1^2   =  16C2  - 4C2^2

4C1 ( 4 - C1) =  4C2 ( 4 - C2)       divide by 4

C1 (4 - C1) =  C2 (4 - C2)      rearrange   as

C2 / C1  =  (4 - C1) / (4 - C2)  implies that

C2 =  4 - C1       and    C1  = 4 - C2      which  both imply that

C1 + C2  =   4

Rearrange as

x^2 -6y +y^2 - 14y   =  -33      complete the square on x and y

x^2  - 6y + 9    +  y^2 - 14y  + 49   =    -33 + 9 + 49

(x - 3)^2  + (y  - 7)^2  =    25

This is a circle centered at  (  3, 7)  with a radius of 5

The part lying below y  = 7 is the  area of 1/2 of this circle  =

pi * 5^2  / 2   =

(25/2)pi ≈  39.3  units^2

The "formula"  for finding the new points is as follows

New Point  = [  Old Point - Dilation Center ] *Scale Factor + Dilation Center

Here's the first one.....you should be able to do the other three based on this....if not, let me know

Note that  (a, b)  - (c, d)  = ( a - c , b - d)       and  (a , b) + (c , d)  = (a + c , b + d)

Here's the dilation result for  (4,7) 

New Point =  [  (4, 7)  - ( 1, -2) ] * 13  +  (1,-2)

=   [  ( 3, 9) ] * 13  +  (1,-2)

=    (39, 117 )  +  (1, -2)

=  (40, 115)