If the distance from the center of dilation to one line is 9, and the distance from the center of dilation to a parallel line is 2.5, what scale factor should be used to map the first line onto the second?

Question

1. The scale factor is equal to half the distance to the original image, 9/2=4.5
2. The scale factor is the distance of the original image, 2.5x9=22.5
3. The scale factor is the distance of the mapped image over the distance of the original image, 2.5/9=0.28
4. The scale factor is the distance of the original image over the distance of the mapped image, 9/2.5=3.6

Answer 1

is the center of dilation between the lines, or are both lines on the same side of the center?

Is only the first line being affected by the new scale?
If both lines, then they can never be mapped onto each other just by scaling.

Answer 2

oobleck whats the answer?

Answer 3

1. the scale factor is the distance of the mapped image over the distance of the original image, 2.5/9 ≈ 0.28
2. the dilated lines are perpendicular
3. 3/2
4. the two triangles are similar because similarity transformations preserve angles and produce proportional distances in a figure.
5. the two triangles are similar. by the interior angles theorem, m<c = 67°, so the triangles are similar by the as similarity criterion
6. pnk ~ kgd by the sas similarity criterion
7. no, yes, yes
8. abc ~ adb by the aa similarity criterion; ab = 8
9. a reflection followed by dilation
10. own essay question
11. own essay question

if you need help with the essay questions lemme know :)

Answer 4

alr., all f them are correct except #7
#7 is;
Proportional corresponding sides- yes
Congruent corresponding angles- yes
Congruent corresponding sides- no