Question

1.After a dilation with a center of (0, 0), a point was mapped as (1, 4) → (4, y). A student determined y to be 16. Evaluate the student's answer.

A.
The student is correct.
B.
The student incorrectly calculated the scale factor to be 4.
C.
The student incorrectly multiplied by the scale factor instead of adding it.
D.
The student incorrectly added the scale factor instead of multiplying by it.

2.Under a dilation centered at the origin, the image is congruent to the preimage. What is the scale factor?

A.
–1 or 0
C.
only 1
B.
0 or 1
D.
–1 or 1

Answer 1

1. The correct option is A.

2. The correct option is D.

Explanation:

1.

If a figure dilated with a center of (0, 0) and scale factor k, then

`(x,y)\rightarrow (kx,ky)`

It is given that

`(1,4)\rightarrow (4,y)`

Scale factor is

`k=(x')/(x)=(4)/(1)=4`

Therefore the scale factor is 4. y-coordinate of image is calculated as

`ky=4* 4=16`

Therefore value of y is 16 and the student is correct. Option A is correct.

2.

If a figure dilated with a center of (0, 0) and scale factor k, then

`(x,y)\rightarrow (kx,ky)`

If |k|>1, then it represent enlargement. If |k|<1, then it represent compression.

If |k|=1, then the image is congruent to the preimage.

At
`k=1` and
`k=-1`, the image is congruent to the preimage. Option D is correct.

Answer 2

Please see below answers:
For question 1 the answer is letter A which is "The student is correct" because they used the scale factor of 4.

For question 2 the answer is letter is D which is –1 or 1 because any point, for example (10,6) would stay at (10,6), making the image the same as the preimage