Math Is Fun Forum

ThatOneKid

Member

Registered: 2015-05-07

Posts: 1

Transformations

Could someone explain how I should solve these problems.

16. After a dilation, (66,6) is the new image from the original (11,1). What are the coordinates of the image of (1,3) after the same dilation?

17. What is the image of triangle PTJ (1, -0), (11, -11), and (7, 7) after a dilation of -7?

18. The translation of triangle BPU (-36, 20), (28, 16), and (8, 12) after a dilation is (9, -5), (-7, -4), and (-2, -3). What is the dilation?

19. The translation of triangle GEP (-4, 10), (-9, -3), and (-6, 6) after a dilation is (-28, 70), (-63, -21), and (-42, 42). What is the dilation?

20. The translation of triangle KTS (6, -36), (-60, 72), and (-54, -36) after a dilation is (1, -6), (-10, 12), and (-9, -6). What is the dilation?

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,432

Website

Re: Transformations

For 16, what do you think the scale factor was?

For 17, how can you apply what you did in 16? (Also, see 18-20 for a clue.)

For 18-20, is there a common scale factor for all three vertices?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Transformations

hi ThatOneKid

In a 'dilation' a point is set as the 'centre of enlargement'.  Let's call it C.  Then you need a scale factor, such as x2.

If A is a point that is dilated to point B, then CB = CA x the scale factor.

So if you wanted to be pedantic, you could say that it's impossible to answer Q16 and Q17 as you were not told the centre.  By taking different points as the centre, I could get an infinite number of answers.

But, looking at these questions, I expect the questioner intended you to take (0,0) as the centre. 
(These weren't from CompuHigh by any chance? *** )

So the x coordinate of 11 has become 66, and the y coordinate of 1 has become 6.  So it looks like the scale factor is x6.

So all you need do, is to multiply the two coordinates of (1,3) each by 6 to get the new coordinates.

For Q17, the scale factor is x -7.  So multiply the coordinates by minus 7.  If you try plotting the old and new points, you should find the new triangle is now on the other side of (0,0).

in Q18, the scale factor is a fraction, so the new triangle is smaller than the original.

And so on.

Note:  The questioner has said the shapes are translated.  That is not the correct word to use ***.  He/she should have said transformation. 
A translation is something else entirely:

http://www.mathsisfun.com/geometry/transformations.html

Hope that helps.  :)  Post your answers if you want them to be checked.

Bob

*** Now I'm even more suspicious about the source of these questions.

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob