calculate the correspondence of spot A (1, 2) to the ratio of spot M (-1, 4)

To calculate the correspondence of spot A (1, 2) to the ratio of spot M (-1, 4), we first need to understand what is meant by "correspondence to the ratio". Here, it can be interpreted as finding the ratio of the distances or coordinates between these two points. Let's calculate both to provide a comprehensive answer:

1. **Ratio of the Coordinates:**

   For points A (1, 2) and M (-1, 4):
   
   - The x-coordinates ratio: \( \frac{x_A}{x_M} = \frac{1}{-1} = -1 \)
   - The y-coordinates ratio: \( \frac{y_A}{y_M} = \frac{2}{4} = \frac{1}{2} \)

2. **Distance Between the Points:**

   The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
   \[
   \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
   \]

   Using the coordinates of points A and M:
   \[
   \text{Distance} = \sqrt{((-1) - 1)^2 + (4 - 2)^2} = \sqrt{(-2)^2 + 2^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2}
   \]

Thus, the correspondence of spot A to spot M involves:
- The coordinate ratios of -1 (for x-coordinates) and \(\frac{1}{2}\) (for y-coordinates).
- The distance between A and M is \(2\sqrt{2}\).

Would you like more details or have any questions?

Here are some related questions you might want to ask:
1. How do you calculate the midpoint between two points?
2. How do you find the slope of the line through two points?
3. What is the formula for the equation of a line passing through two points?
4. How do you determine if two lines are parallel or perpendicular?
5. How do you convert coordinates from Cartesian to polar form?

**Tip:** When working with coordinates, always pay close attention to signs (positive or negative) as they significantly impact calculations.

Learn how to calculate the correspondence of point A (1, 2) to the ratio of point M (-1, 4) using coordinate geometry and the distance formula. Understand the ratio of coordinates and the distance between two points. Suitable for high school students.

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