Week 3 Assignment: Distance Formula X X2 Y Y2 Find The Dis

Week 3assignment Distance Formulad X X2 Y Y2find The Dis

Identify and compute the distances between pairs of points using the distance formula, which is d = √[(x₂ - x₁)² + (y₂ - y₁)²]. Given pairs include (1, 2) and (3, ?), (-2, 3) and (4, ?), (4, -3) and (2, ?), (1, 3) and (4, 7). For each pair, substitute the x and y coordinates into the formula to find the Euclidean distance.

Paper For Above instruction

The task involves calculating the distances between various pairs of points in a two-dimensional plane using the distance formula derived from the Pythagorean theorem. This formula allows us to quantify how far apart two points are in a coordinate system, which is fundamental in fields ranging from geometry to data analysis.

The distance formula is expressed as d = √[(x₂ - x₁)² + (y₂ - y₁)²], where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points. Applying this formula, mathematical calculations enable us to determine the exact Euclidean distance between each pair.

For example, to find the distance between points (1, 2) and (3, ?), first identify the difference in the x-coordinates: 3 - 1 = 2. Next, subtract the y-coordinates: ? - 2. The distance is then √[2² + (? - 2)²], which simplifies to √[4 + (? - 2)²]. To complete this computation, the missing y-coordinate in the second point must be known or clarified. Similarly, for each pair, substitute the known x and y values into the formula, calculate differences, square these differences, and sum them before taking the square root.

Applying the distance formula provides a precise measure, which is essential in various applications such as navigation, computer graphics, and spatial analysis. Proper understanding ensures correct computation of distances, crucial for accurate modeling and analysis of data points.

In educational applications, mastering this formula enhances students' geometric understanding and problem-solving skills. This foundational concept also supports more advanced mathematical topics, including vector analysis and multivariate statistics.

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