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.
