Determine whether the dilation passes through the center of dilation.

Question

(1 point)
Responses

A′B′¯¯¯¯¯¯¯¯¯¯
passes through the center of dilation because it is an enlargement of AB¯¯¯¯¯¯¯¯
by a scale factor of 4.
line segment cap A prime cap b prime passes through the center of dilation because it is an enlargement of line segment cap A cap b by a scale factor of 4.

A′B′¯¯¯¯¯¯¯¯¯¯
does not pass through the center of dilation because it is a reduction of AB¯¯¯¯¯¯¯¯
by a scale factor of 14
.
line segment cap A prime cap b prime does not pass through the center of dilation because it is a reduction of line segment cap A cap b by a scale factor of Start Fraction 1 over 4 End Fraction .

A′B′¯¯¯¯¯¯¯¯¯¯
passes through the center of dilation because it is taken to a line parallel to AB¯¯¯¯¯¯¯¯
.
Modifying above upper A prime upper B prime with bar passes through the center of dilation because it is taken to a line parallel to Modifying above upper A upper B with bar .

A′B′¯¯¯¯¯¯¯¯¯¯
does not pass through the center of dilation because it is taken to a line parallel to AB¯¯¯¯¯¯¯¯
.
Modifying above upper A prime upper B prime with bar does not pass through the center of dilation because it is taken to a line parallel to line segment cap A cap b .

Answer 1

To determine whether the dilation passes through the center of dilation, we need to understand how dilations work in geometry.

1. When a line segment AB is dilated from a center of dilation point O, the image A'B' will be formed. If the scale factor is greater than 1, it is an enlargement, and if it is less than 1, it is a reduction.

2. A dilation with respect to a point (center of dilation) means that each point on the line segment moves closer to (or further away from) that point based on the scale factor.

• If the line segment A'B' includes point O, then we say A'B' passes through the center of dilation.
• If A'B' does not include point O, then A'B' does not pass through the center of dilation.

Based on the given responses, we can analyze each one:

1. A′B′ passes through the center of dilation because it is an enlargement of AB by a scale factor of 4.

   • This could indicate that A'B' passes through the center if the center is on the segment or aligned accordingly.

2. A′B′ does not pass through the center of dilation because it is a reduction of AB by a scale factor of 1/4.

   • This would imply that it’s unlikely for A'B' to include the center if it’s a reduction and does not maintain alignment with the original line segment.

3. A′B′ passes through the center of dilation because it is taken to a line parallel to AB.

   • A dilation involving a line drawn through the center leads to the conclusion that line segments remain proportionate; however, this does not necessarily confirm passing through the center.

4. A′B′ does not pass through the center of dilation because it is taken to a line parallel to AB.

   • If A'B' is transformed into a line parallel to AB and does not intersect the center of dilation, this result aligns with the idea that it does not pass through O.

To summarize, if A'B' is an enlargement or reduction based on whether it maintains direct alignment with the center of dilation while including or excluding it, we can determine if it passes through the center:

Conclusion: If A'B' is simply parallel to X and does not include O, then the correct response is that A′B′ does not pass through the center of dilation because it is taken to a line parallel to AB.

Answer 2

Why in dice dreams didn’t I get my prize for getting #3 in the tournament thingy?

Answer 3

In games like Dice Dreams, not receiving a prize for a certain achievement, such as ranking #3 in a tournament, can happen for a few reasons:

1. Technical Issues: There may have been a glitch or issue with the game that prevented your prize from being awarded.

2. Timing: Sometimes, rewards are distributed based on specific timing. If you reached your rank after the prize distribution deadline, you might not receive a reward.

3. Game Rules: It's possible that there are specific eligibility requirements for receiving prizes that you may not be aware of. Always check the tournament rules or FAQs to ensure that you meet all criteria.

4. Server Issues: If the server was experiencing issues at the time the rankings were updated or rewards were distributed, it might have affected your ability to receive your prize.

5. Updates or Changes: Developers occasionally change prize structures or distributions during updates. If the game has had recent updates, it might have altered the prize distribution.

If you believe you should have received the prize, it’s a good idea to check the game’s official support or help section, where you can report the issue. They may be able to provide an explanation or rectify the situation.