Question

Line AB
and line CD
are parallel lines. Line AB
contains the points A(1,−5)
and B(4,−2)
, and line CD
contains the points C(−1,0)
and D(2,3)
. Describe the effect of the dilation with a scale factor of 5 and a center point of dilation at the origin (0,0)
.(1 point)
Responses

After dilation, the lines are five units farther from the point of dilation. The resulting points are A′ (6,0)
, B′ (9,3)
, C′(4,5)
, and D′(7,8)
. The dilated lines are parallel.
After dilation, the lines are five units farther from the point of dilation. The resulting points are upper A prime left parenthesis 6 comma 0 right parenthesis , upper B prime left parenthesis 9 comma 3 right parenthesis , upper C prime left parenthesis 4 comma 5 right parenthesis , and upper D prime left parenthesis 7 comma 8 right parenthesis . The dilated lines are parallel.

After dilation, the lines are five units closer to the point of dilation. The resulting points are A′ (5,−25)
, B′ (20,−10)
, C′(−5,0)
, and D′(10,15)
. The dilated lines are parallel.
After dilation, the lines are five units closer to the point of dilation. The resulting points are upper A prime left parenthesis 5 comma negative 25 right parenthesis , upper B prime left parenthesis 20 comma negative 10 right parenthesis , upper C prime left parenthesis negative 5 comma 0 right parenthesis , and upper D prime left parenthesis 10 comma 15 right parenthesis . The dilated lines are parallel.

After dilation, the lines are five units closer to the point of dilation. The resulting points are A′ (15,1)
, B′(45,−25)
, C′(−15,0)
, and D′(23,35)
. The dilated lines are parallel.
After dilation, the lines are five units closer to the point of dilation. The resulting points are upper A prime left parenthesis Start Fraction 1 over 5 End Fraction comma 1 right parenthesis , upper B prime left parenthesis Start Fraction 4 over 5 End Fraction comma negative Start Fraction 2 over 5 End Fraction right parenthesis , upper C prime left parenthesis Start Fraction negative 1 over 5 End Fraction comma 0 right parenthesis , and upper D prime left parenthesis Start Fraction 2 over 3 End Fraction comma Start Fraction 3 over 5 End Fraction right parenthesis . The dilated lines are parallel.

After dilation, the lines are five units farther from the point of dilation. The resulting points are A′ (5,−25)
, B′ (20,−10)
, C′(−5,0)
, and D′(10,15)
. The dilated lines are parallel.

Answer 1

To analyze the effect of the dilation with a scale factor of 5 and a center point at the origin (0,0), we need to apply the dilation transformation to points A, B, C, and D.

The dilation formula with center at the origin is:
\[
(x', y') = (kx, ky)
\]
where \( k \) is the scale factor. In this case, \( k = 5 \).

### Applying Dilation:
1. **Point A (1, -5)**:
\[
A' = (5 \cdot 1, 5 \cdot -5) = (5, -25)
\]

2. **Point B (4, -2)**:
\[
B' = (5 \cdot 4, 5 \cdot -2) = (20, -10)
\]

3. **Point C (-1, 0)**:
\[
C' = (5 \cdot -1, 5 \cdot 0) = (-5, 0)
\]

4. **Point D (2, 3)**:
\[
D' = (5 \cdot 2, 5 \cdot 3) = (10, 15)
\]

### Conclusion:
So the resulting points after dilation are:
- \( A' (5, -25) \)
- \( B' (20, -10) \)
- \( C' (-5, 0) \)
- \( D' (10, 15) \)

The dilated lines will remain parallel because dilation preserves the orientation and parallelism of lines.

### Correct Response:
After dilation, the lines are five units farther from the point of dilation. The resulting points are \( A' (5, -25) \), \( B' (20, -10) \), \( C' (-5, 0) \), and \( D' (10, 15) \). The dilated lines are parallel.