Match the points A, B, and C with their coordinates from the given options.

Solution:

We need to match the points on the number line with their corresponding coordinates. Let's analyze the number line:

• The point labeled '0' is the origin.
• The point labeled '-1' is to the left of the origin.
• Point B is to the right of -1 and to the left of 0. Observing the spacing, it appears to be at -0.5. However, the options are fractions or mixed numbers, so let's re-evaluate based on the provided options and the general layout.
• Point C is to the left of -1. It appears to be around -1.5 or -2.
• Point A is further to the left, appearing to be around -3 or -4.

Let's examine the coordinate options:

1. -3, 2
2. -18/7
3. -9/5
4. -5/7
5. 1 3/8

Now, let's try to align the points with the options:

• Option 1: '-3, 2' - This seems to have two coordinates, which doesn't fit a single point on a 1D number line. However, if we consider '-3' as a potential coordinate, it aligns with where point A might be. The '2' is likely extraneous or a typo if it's meant for a single point.
• Option 2: '-18/7' is approximately -2.57. This could potentially match point C.
• Option 3: '-9/5' is -1.8. This also could potentially match point C.
• Option 4: '-5/7' is approximately -0.71. This could match point B.
• Option 5: '1 3/8' is 1.375. This is a positive value and does not match any of the points A, B, or C, which are all on the negative side of the number line.

Let's assume the question intends to match point names with coordinates. Looking closely at the number line, we can estimate:

• Point A is to the left of -1, likely around -3.
• Point C is between -1 and 0. It looks closer to -1.5 or -2.
• Point B is between -1 and 0, and appears to be closer to 0 than -1, perhaps around -0.5.

Let's re-evaluate the options based on these estimations:

• If A is -3, then option 1 (-3, 2) has a -3. Let's tentatively assign A to -3.
• If B is around -0.5, then -5/7 (approx -0.71) or maybe even -9/5 (-1.8) could be considered, but -5/7 is closer to -0.5.
• If C is around -1.5 to -2, then -18/7 (approx -2.57) or -9/5 (-1.8) are possibilities.

Let's reconsider the image. The points are marked with purple dots. The spacing between ticks seems to be 1 unit. Point B is clearly to the right of -1 and to the left of 0. It looks to be closer to -1 than to 0. Let's say it's around -0.7. Option 4: -5/7 is approximately -0.71. This seems like a good match for B.

Point C is to the left of -1. It looks to be around -1.8 to -2. Option 3: -9/5 is -1.8. This seems like a good match for C.

Point A is further to the left, clearly more negative than -2. If C is -1.8 and B is -0.7, and given the spacing, A looks to be around -3. Option 1: -3, 2. If we consider only the -3 part, it matches A. The '2' is problematic. However, if we have to choose the best fit, the '-3' for point A is strong.

Let's assume there might be a typo and the question is asking to match A, B, C to a subset of these coordinates.

Let's try to match based on position relative to -1 and 0.

• B is between -1 and 0. Option 4 (-5/7 ≈ -0.71) is in this range.
• C is to the left of -1. It appears to be around -1.5 to -2. Option 3 (-9/5 = -1.8) is in this range.
• A is further left. It appears to be around -3. Option 1 (-3, 2) has -3.

Given these pairings, we have:

• A: -3 (from option 1)
• B: -5/7 (option 4)
• C: -9/5 (option 3)

The problem states "Помоги учёным установить соответствие между точками и их координатами." (Help scientists establish correspondence between points and their coordinates). This implies a one-to-one mapping. The presence of '2' in option 1 and option 5 being a positive mixed number are confusing.

Let's assume the most direct visual interpretation of the number line:

• Point B is visually slightly to the left of the midpoint between -1 and 0. So, something around -0.6 or -0.7. Option 4: -5/7 ≈ -0.71.
• Point C is visually to the left of -1, appearing to be around -1.8. Option 3: -9/5 = -1.8.
• Point A is visually around -3. Option 1: -3, 2. The '-3' part aligns.

Therefore, a likely matching would be:

• A corresponds to -3 (from option 1).
• B corresponds to -5/7 (option 4).
• C corresponds to -9/5 (option 3).

We will use these pairings.

Matching:

• Point A corresponds to coordinate 1. (-3)
• Point B corresponds to coordinate 4. (-5/7)
• Point C corresponds to coordinate 3. (-9/5)

Note: Option 2 (-18/7 ≈ -2.57) and Option 5 (1 3/8 = 1.375) do not seem to match any points based on their visual positions on the number line. The '2' in option 1 is also unassigned.