The task is to match the points A, B, and C on the number line with their corresponding coordinates from the given options. The number line shows points A, C, and B. Point B is located at -1. Point 0 is to the right of -1, and point C is between A and B. Point A is to the left of C. The options for coordinates are: 1. -3,2, 2. -18/7, 3. -9/5, 4. -5/7, 5. 1 3/8. Based on the visual representation of the number line: - Point B is at -1. - Point 0 is to the right of B. - Since C is to the left of B and to the right of A, and B is at -1, C must be a negative number greater than -1. For example, if A is at -3, then C could be around -0.5 or -0.75. - Point A is to the left of C and is likely a negative number with a larger absolute value than C and B. Let's evaluate the options: 1. -3,2: This appears to be two separate values, not a single coordinate. If it means -3.2, it could potentially be A. 2. -18/7 ≈ -2.57. This could potentially be A. 3. -9/5 = -1.8. This is to the left of -1 (B), but to the right of -2.57 (option 2). This might be C if B was further left, or A if B was closer to 0. 4. -5/7 ≈ -0.71. This is to the right of -1 (B), which contradicts the visual that B is at -1 and C is to the left of B. If B is indeed at -1, then C should be a negative number greater than -1 (closer to 0) or A should be even further left. Looking at the image, B is clearly marked at -1. C is to the left of B, and A is to the left of C. So C should be < -1 and A should be < C. Wait, looking closer at the number line, point B is at -1. Point 0 is to the right. Point C is to the left of B. Point A is to the left of C. Therefore, A < C < B < 0. So A, C and B must all be negative. Let's re-examine the options and the number line: - B is at -1. - C is to the left of B. So C < -1. - A is to the left of C. So A < C. This means A and C must be negative numbers with magnitudes greater than 1. Let's re-evaluate the options based on this: 1. -3,2: If interpreted as -3.2, this could be A. 2. -18/7 ≈ -2.57. This could be A or C. 3. -9/5 = -1.8. This could be C. 4. -5/7 ≈ -0.71. This is GREATER than -1, so it cannot be C or A if B is at -1. 5. 1 3/8 = 1.375. This is positive, so it cannot be A, B, or C. This implies there might be an issue with option 4 or the visual representation of C. Let's assume the markings on the number line are accurate and B is exactly at -1. A < C < B < 0 A < C < -1 < 0 From the options, we have: - A could be -3.2 (option 1) or -18/7 ≈ -2.57 (option 2). - C could be -1.8 (option 3). If A = -18/7 (≈ -2.57) and C = -1.8, then A < C < -1. This fits the order. If A = -3.2 (option 1) and C = -1.8 (option 3), then A < C < -1. This also fits the order. Let's look at the spacing on the number line. The distance between -1 and 0 looks similar to the distance between -1 and the point to its left (C), and the distance between C and A looks roughly similar or larger. If C = -1.8, then the distance from C to B (-1) is 0.8. The distance from B (-1) to 0 is 1. The point C is slightly more than halfway between -1 and -2. If A = -3.2, the distance from A to C is |-1.8 - (-3.2)| = 1.4. The distance from C to B is |-1 - (-1.8)| = 0.8. This means A is significantly further left than C, and C is to the left of B. This looks plausible on the diagram. If A = -18/7 (≈ -2.57) and C = -9/5 (-1.8), then the distance from A to C is |-1.8 - (-2.57)| = 0.77. The distance from C to B is |-1 - (-1.8)| = 0.8. This implies A and C are very close in distance to B, with A being slightly closer to C than C is to B. This also looks plausible. Let's reconsider the options and the labels: Points: A, B, C Coordinates: 1. -3,2, 2. -18/7, 3. -9/5, 4. -5/7, 5. 1 3/8. B is at -1. C is to the left of B. So C < -1. A is to the left of C. So A < C. Re-evaluating options: Option 1: -3,2. This is written strangely. If it means -3.2. Then it could be A. Option 2: -18/7 ≈ -2.57. This could be A. Option 3: -9/5 = -1.8. This could be C. Option 4: -5/7 ≈ -0.71. This is to the RIGHT of -1, so it CANNOT be A or C. Option 5: 1 3/8 = 1.375. This is POSITIVE, so it CANNOT be A, B, or C. This leaves options 1, 2, and 3 as potential candidates for A and C, with B being -1. Since B is at -1: C must be less than -1. -9/5 = -1.8 is a possibility for C. A must be less than C. -18/7 ≈ -2.57 is a possibility for A. -3.2 (from option 1) is also a possibility for A. If C = -1.8, and A = -2.57, then A < C < B is satisfied. If C = -1.8, and A = -3.2, then A < C < B is satisfied. Let's look at the visual spacing more closely. The distance from C to B (0.8 if C=-1.8) appears slightly less than the distance from A to C (1.4 if A=-3.2, or 0.77 if A=-2.57). If C = -1.8 and A = -3.2, then the distance A to C is 1.4, and C to B is 0.8. The ratio is roughly 1.4 / 0.8 = 1.75. The visual spacing looks like A is roughly twice as far from C as C is from B, or slightly less. This makes A=-3.2 a strong candidate for A, and C=-1.8 a strong candidate for C. Let's verify this: B = -1 (given on the number line) C = -9/5 = -1.8 A = -3,2 (interpreted as -3.2) Check order: -3.2 < -1.8 < -1. This matches A < C < B. So, the matches are: A corresponds to -3.2 (option 1, interpreting as a single decimal number). B corresponds to -1 (marked on the number line, but not an option - this is a problem. Ah, the question is asking to match points to COORDINATES, and the points are A, B, C. The options are the coordinates. B is marked at -1. So B must correspond to a coordinate that is -1. However, -1 is not listed as an option. Let me re-read: "Помоги учёным установить соответствие между точками и их координатами." "Help the scientists establish the correspondence between points and their coordinates." So we have points A, B, C and coordinate options 1, 2, 3, 4, 5. The number line shows A, C, B and marks -1 and 0. B is at -1. This means B *is* coordinate -1. Since -1 is NOT an option, there might be a misunderstanding or an error in the problem. Let's assume the options are the ONLY possible coordinates and the number line is just a visual aid that might not perfectly align with the options, EXCEPT for the ordering and relative positions. But B is explicitly at -1. Let's consider the possibility that the question implies that the options *are* the coordinates for A, B, and C, and we need to pick which option corresponds to which letter. The number line helps establish the order. A < C < B < 0. This means A, C, and B are all negative. Let's revisit the options: 1. -3,2 (assuming -3.2) 2. -18/7 ≈ -2.57 3. -9/5 = -1.8 4. -5/7 ≈ -0.71 (Positive magnitude is less than 1, so it's between -1 and 0. This CANNOT be A or C, as they are to the left of B=-1). 5. 1 3/8 = 1.375 (Positive, cannot be A, B, or C). So, options 4 and 5 are definitely OUT. This leaves options 1, 2, and 3 for A, B, and C. We know B is at -1 on the number line. If B is one of the options, it must be the one closest to -1 or somehow representing -1. None of the options are -1. This is still problematic. However, if we strictly match the *order* from the number line (A < C < B < 0) with the *values* from the options, and assume the options are *all* the possible coordinates for A, C, and *perhaps B*, even if B's position on the line seems exact. We need three negative numbers from options 1, 2, 3 that are in increasing order (A < C < B). Let's order the negative options: -3.2 (Option 1) -18/7 ≈ -2.57 (Option 2) -9/5 = -1.8 (Option 3) So, the order from smallest to largest (most negative to least negative) is: -3.2 < -2.57 < -1.8. This matches the order A < C < B. Therefore: A corresponds to -3.2 (Option 1). C corresponds to -2.57 (Option 2). B corresponds to -1.8 (Option 3). This assignment satisfies the order A < C < B, and all are negative. The number line shows B at -1, which is slightly to the right of -1.8. This implies that the visual marking of B at -1 might be approximate, or the options are the definitive coordinates and the number line shows the relative order correctly. Let's assume the options are the correct coordinates and the number line shows their relative positions. So we need to match A, B, C to options 1, 2, 3. Order from number line: A < C < B < 0 Option values (negative ones): 1. -3,2 (interpreted as -3.2) 2. -18/7 (approx -2.57) 3. -9/5 (approx -1.8) Ordering these values: -3.2 < -2.57 < -1.8 So, if A < C < B, then: Point A must be -3.2 (Option 1) Point C must be -18/7 (Option 2) Point B must be -9/5 (Option 3) This assignment perfectly fits the order A < C < B. Let's re-check the visual. If B is at -1.8, then -1 would be to its right. The number line shows 0 to the right of -1. If B is at -1.8, then C at -2.57 and A at -3.2 are to its left, which fits the ordering. The marker for B is exactly on -1. If we must assign options to A, B, C and B is at -1, then none of the options fit B. This means we should ignore the specific value -1 on the number line and only use the relative positions of A, C, B. The relative positions are A < C < B. So, mapping the ordered options to the ordered points: A -> 1. -3,2 (or -3.2) C -> 2. -18/7 B -> 3. -9/5 This seems to be the most logical interpretation if we must use the provided options.