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?
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
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 :)
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.
oobleck whats the answer?
alr., all f them are correct except #7
#7 is;
Proportional corresponding sides- yes
Congruent corresponding angles- yes
Congruent corresponding sides- no
The correct answer is option 4. The scale factor is the distance of the original image over the distance of the mapped image, which is 9/2.5. To understand why, let's break it down step by step:
- In a dilation, the scale factor determines how much the original figure is enlarged or reduced to create the mapped figure.
- The scale factor can be calculated by comparing the distances from the center of dilation to corresponding points on the original and mapped figures.
Given that the distance from the center of dilation to the first line is 9, and the distance from the center of dilation to the second line is 2.5, we need to find the scale factor.
The scale factor is defined as the ratio of the distance of the original image to the distance of the mapped image. In this case, the distance of the original image is 9, and the distance of the mapped image is 2.5.
Therefore, the scale factor is 9 divided by 2.5, which equals 3.6. This means that the second line is 3.6 times shorter than the first line when mapped using the given dilation.
So, the correct answer is option 4, which states that the scale factor is 9 divided by 2.5, or 3.6.