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2 years ago

NO LINKS OR ASSESSMENT!!Write a rule to describe each transformation #9 & #11

Mathematics

2 answers:

ValentinkaMS [17]2 years ago

8 0

Answer:

Step-by-step explanation:

Remark

I really don't know what to write to these questions. I can never tell what the problem is. Perhaps it is right at the very beginning. You have to recognize what is taking place. In problem 9, the easiest point to follow is H going to H'. Do you see what is happening? H is sitting on the x axis and then something happens to it and behold, it is now sitting on the y axis. So it has rotated 90 degrees but which way?

Take your finger or a pencil and put it on H. Then make a circular motion to get to H'. You are going clockwise. (keep going in that direction till you wind up where you started. You are going in the direction of one of those old fashioned clocks. Now the trick in a rotation is if you can figure out what one point is doing, you know what all points are doing on the given figure.

So the translation is 90 degrees clockwise. That means the following rule must be operating

(x,y) ===> (y, - x)

H(-3,0) ===> H'(0, - - 3) = H'(0,3)

I(-2,1) =====>I'(1, - - 2) = H'(1,2)

J(0,1) =====>J'(1,0)

G(-3,-3)====>G'(-3, --3) = G'(-3,3)

At first you may think that this is a translation of some kind. I thought so at first. D and D' certainly look that way and C and C' also look that way. But B and E are not well behaved. You are looking at a 180 degree rotation

The rule you need here is (x,y) becomes (-x , - y)

I'll leave C and D to you and do one of the B and E

E(3,5)=E'(-3 , - 5)

Vikentia [17]2 years ago

6 0

9514 1404 393

Answer:

9) (x, y) ⇒ (y, -x) . . . . rotation 90° CW

11) (x, y) ⇒ (-x, -y) . . . rotation 180°

Step-by-step explanation:

9) Distance from the origin to an image point is the same as to the preimage point, but the direction is changed by 90° in the CW direction. For example, J is north of the origin, but J' is east, a direction change of 90° CW.

The transformation describing a 90° CW rotation is the rule ...

(x, y) ⇒ (y, -x)

11) Distance and direction to each image point from the origin are equal and opposite of distance and direction to the preimage point. The figure has been rotated 180°. The corresponding rule is ...

(x, y) ⇒ (-x, -y)

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Answer: The numbers are: " 21 " and " 105 " .
___________________________________________________
Explanation:
___________________________________________________
Let "x" be the "one positive number:

Let "y" be the "[an]othyer number".

x = 1/5 (y)
___________________________________________________
Given that the difference of the two number is "84" ; and that "x" is (1/5) of "y" ; we determine that "x" is smaller than "y".

So, y − x = 84 .

Add "x" to each side of this equation; to solve for "y" in terms of "x" ;

y − x + x = 84 + x ;

y = 84 + x ;
___________________________________________________
So, we have:

x = (1/5) y ;

and: y = 84 + x ;

Substitute "(1/5)y" for "x" ; in "y = 84 + x " ; to solve for "y" ;

y = 84 + [ (1/5)y ]

Subtract " [ (1/5)y ] " from EACH SIDE of the equation ;

y − [ (1/5)y ] = 84 + [ (1/5)y ] −  [ (1/5)y ] ;

to get:

[ (4/5)y ] = 84 ;

       ↔    (4y) / 5 = 84 ;

        → 4y = 5 * 84 ;

      Divide EACH SIDE of the equation by "4" ;
to isolate "y" on one side of the equation; and to solve for "y" ;

           4y / 4 = (5 * 84) / 4 ;

                 y = 5 * (84/4) = 5 * 21 = 105 .

   y = 105 .
___________________________________________________
Now, plug "105" for "y" into:
___________________________________________________
Either:
___________________________________________________
x = (1/5) y ;

OR:

y = 84 + x ;
___________________________________________________
to solve for "x" ;
___________________________________________________
Let us do so in BOTH equations; to see if we get the same value for "x" ; which is a method to "double check" our answer ;
___________________________________________________
Start with:

x = (1/5)y

    → (1/5)*(105) = 105 / 5 = 21 ; x = 21 ;

___________________________________________________
So, x = 21; y = 105 .
___________________________________________________
Now, let us see if this values hold true in the other equation:
___________________________________________________
y = 84 + x ;

105 = ? 84 + 21 ?

105 = ? 105 ? Yes!
___________________________________________________
The numbers are: " 21 " and "105 " .
___________________________________________________

6 0

3 years ago

NO LINKS OR ASSESSMENT!!Write a rule to describe each transformation #9 & #11​

NO LINKS OR ASSESSMENT!!Write a rule to describe each transformation #9 & #11