Determine the scale factor of the following dilation. d o, k (9, 6) → (3, 2)

Determine the scale factor of the following dilation.
d o, k (9, 6) → (3, 2)

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  1. The scale factor of the following dilation is:

                                1/3

    Step-by-step explanation:

    Dilation--

    A dilation is a transformation which changes the size of the original figure.

    It either shrinks or enlarges the figure by some fixed factor.

    This factor is known as a scale factor.

    Also, if the scale factor is k and the dilation is about the origin.

    Then any point (x,y) is transformed to point (kx,ky).

    Here (9,6) is transformed to (3,2) and the dilation is about the origin.

    This means that:

      (9,6) → (9k,6k)

    i.e.

    (3,2) = (9k,6k)

    i.e.

    9k=3    and   6k=2

    k=3/9   and   k=2/6

    k=1/3  and  k=1/3

    Hence, the scale factor is:  1/3

  2. 1)

    Option b ( (7,2) )

    2)

    Option b ( (-3, 2) )

    3)

    Option b ( (1, 2) )

    4)

    Option: c ( (1, 3)  )

    5)

    Option c (  (6, -2) )

    6)

    option a ( 1/3 )

    7)

    Option b ( (-2, 2) )

    8)

    Option c   (2/3 )

    9)

    Option a ( (-1/2, 3/2) )

    Step-by-step explanation:

    1)

    The image of (4, 1) under the transformation T : (x, y) → (x + 3, y + 1) .

    the point (4,1) is transformed to:

    (4,1) → (4+3,1+1)

    i.e. (4,1) → (7,2)

    Hence, option b is correct.

    2)

    The image of (2, -1) under the transformation T -5, 3 is:

    i.e. any point (x,y) is transformed as:

    (x,y) → (x-5,y+3)

    Hence (2,-1) → (2-5, -1+3)

    i.e. (2,-1) → ( -3, 2)

    Hence, option b is correct.

    3)

    A point is mapped under the transformation T : (x, y) → (x + 3, y + 1).

    Hence the preimage of (4,3) is calculated as:

    (x,y) → (x+3,y+1)= (4,3)

    i.e. x+3=4   and  y+1=3

    i.e. x=4-3   and  y=3-1

    i.e.  x=1 and y=2.

    Hence the preimage of (4,3) is (1,2)

    Hence, option b is correct.

    4)

    If a translation maps point (3, 2) to (4, 5), then what is the image of the point (0, 0).

    Since (3,2) is translated to (4,5) that means the x-value is increased by 1 and y-value is increased by 3.

    i.e. any point (x,y) is transformed to (x+1,y+3).

    Hence, the transformation of (0,0) will be:

    (0,0) → (0+1,0+3)

    i.e. (0,0) → (1,3)

    Hence, option c is correct.

    5)

    The image of (-2, 5) is (1, 1).

    i.e. the translation would be:

    (x,y) → (x+3,y-4)

    Hence, image of  (3, 2) under the same translation will be:

    (3,2) → (3+3,2-4)

    i.e. (3,2) → (6, -2)

    Hence, option c is correct.

    6)

    D O,K (9, 6) → (3, 2)

    i.e. the point (9,6) is dilated to (3,2).

    I.e. if k is a scale factor then (9,6) is dilated to (9k,6k)

    We have (9k,6k)=(3,2)

    i.e. 9k=3

    i.e. k=1/3

    Hence the scale factor is 1/3.

    Hence, option a is true.

    7)

    the image of (-1,1) after a dilation of 2 is:

    (-1,1) → (-1×2,1×2)=(-2,2)

    Hence, (-1,1) → (-2,2)

    Hence, option b is correct.

    8)

    The image of (6, 9) under a dilation is (4, 6).

    if k is a scale factor that means:

    (6k,9k)=(4,6)

    i.e. 6k=4

    k=2/3

    Hence the scale factor is: 2/3

    Hence option c is correct.

    9)

    A dilation maps (4, 6) to (2, 3).

    if k is a scale factor than:

    (4k,6k)=(2,3)

    i.e. 4k=2

    i.e. k=1/2

    Hence, the scale factor is 1/2.

    Hence, the image of (-1,3) under the same dilation is:

    (-1,3) → (-1/2,3/2)

    Hence, option a is true.

  3. The scale factor of the following dilation is, [tex]\frac{1}{3}[/tex]

    Step-by-step explanation:

    The rule of dilation with scale factor k is given by:

    [tex](x, y) \rightarrow (kx, ky)[/tex]

    As per the statement:

    Given the following dilation:

    (9, 6) → (3, 2)                 .....[1]

    We have to find the scale factor.

    Using the above rule we have;

    [tex](9, 6) \rightarrow (9k, 6k)[/tex]

    Now compare this with equation [1] we have;

    (9k, 6k) = (3, 2)

    ⇒9k = 3 or 6k = 2

    After solving both we get;

    [tex]k = \frac{1}{3}[/tex]

    Therefore,  the scale factor of the following dilation is, [tex]\frac{1}{3}[/tex]

  4. A. 1/5

    All the points are simply divided by 5 to get the answer. If it were -1/5, then the new points would be negative. (Or positive for the points initially negative).

  5. 1/3

    Step-by-step explanation:

    Given that original coordinate is (9,6)

    It is transformed into a new coordinate (3,2)

    WE have to find the scale factor of transformation.

    On observing, both the coordinates we find that both coordinates have x and y positive. Hence no reflection on either axis.

    In both x coordinate is bigger than y coordinate. So no rotation about origin.

    COmparison gives new coordinates are 1/3 of original coordinates

    Hence scale factor of dilation = 1/3

  6. (9,6)

    = (3,2)

    3

    This means that the dilation of (9, 6) to (3, 2) is (1/3(x), 1/3(y))

    ⭐ Answered by Hyperrspace (Ace) ⭐

    ⭐ Brainliest would be appreciated, I'm trying to reach genius! ⭐

    ⭐ If you have questions, leave a comment, I'm happy to help! ⭐

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