Question

30 points: 5 star and best answer and thanks. you can leave answers in. A B C or D ty ty ty.

1. The image of (4, 1) under the transformation T : (x, y) → (x + 3, y + 1) is _____. a (1, 0) b (7, 2) c (-1, 0)

2.The image of (2, -1) under the transformation T -5, 3 is _____. a (3, 2) b (-3, 2) c (-3, -2)

3.A point is mapped under the transformation T : (x, y) → (x + 3, y + 1).
What is the preimage of (4, 3)?a (-1, 2) b (1, 2) c (7, 4)

4.If a translation maps point (3, 2) to (4, 5), then what is the image of the point (0, 0)?
a (4, 5)
b (-1, -3)
c (1, 3)



5.The image of (-2, 5) is (1, 1).
What is the image of (3, 2) under the same translation?
a (0, -2)
b (3, -4)
c (6, -2)
d (7, 0)

6.Determine the scale factor of the following dilation.
D O,K (9, 6) → (3, 2)
a 1/3
b 3
c 6

7.What is the image of (-1, 1) after a dilation of 2?
a (1, 3)
b (-2, 2)
c (2, 2)

8.The image of (6, 9) under a dilation is (4, 6).
The scale factor of the dilation is _____.
a 2 b (3/2) c (2/3)

9.A dilation maps (4, 6) to (2, 3).
Under the same dilation, (-1, 3) would be mapped to _____.
a (-1/2, 3/2)
b (-3, 0)
c (-2, 6)

Answer 1

1, B 2, C 3, C 4, C 5, a 6, b 7, b 8, C 9, a I think. Hoped this helps.

Answer 2

Answer:

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.