How to Calculate the Distance Between Two Points: A Student's Guide
Quick Answer
To find the distance between two points, like (2, 4) and (5, 5), use the distance formula: √[(x2 - x1)² + (y2 - y1)²]. For these points, the distance is √10 units.
Calculating the distance between two points on a coordinate plane is a fundamental concept in geometry. The distance formula allows you to determine how far apart two points are, which is useful in various real-world applications such as navigation, architecture, and computer graphics.
The distance formula is given by:
$$d = ext{√}[(x_2 - x_1)^2 + (y_2 - y_1)^2]$$
where \(d\) represents the distance between the two points (\(x_1, y_1\)) and (\(x_2, y_2\)).
Let’s break down how to use this formula with an example:
Suppose we have two points on a graph: (2, 4) and (5, 5). We’ll label these as follows:
- Point 1: (x1, y1) = (2, 4)
- Point 2: (x2, y2) = (5, 5)
Now, plug these values into the distance formula:
1. First, subtract the x-coordinates: \(x_2 - x_1 = 5 - 2 = 3\)
2. Then, subtract the y-coordinates: \(y_2 - y_1 = 5 - 4 = 1\)
3. Next, square both results:
- \((x_2 - x_1)^2 = 3^2 = 9\)
- \((y_2 - y_1)^2 = 1^2 = 1\)
4. Add the squares together: \(9 + 1 = 10\)
5. Finally, take the square root of the sum:
- \(d = ext{√}10\)
Thus, the distance between the points (2, 4) and (5, 5) is \(√10\) units.
This method can be applied to any two points you encounter. For instance, if you were to find the distance between the points (1, 2) and (4, 6), you would follow the same steps, resulting in a distance of \(√(3^2 + 4^2) = √(9 + 16) = √25 = 5\) units.
Understanding how to calculate distances is essential, especially when dealing with problems in geometry, physics, and even computer science. Whether you're plotting points on a graph, designing a layout for a building, or programming a game, knowing how to measure distances accurately will enhance your problem-solving skills.
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