Introduction:

Calculating the distance between two points in a two-dimensional coordinate system is crucial in geometry. This calculation, known as the Euclidean distance, is widely used in various applications such as mapping and computer graphics.



Simple Explanation:



What is the Distance Formula?



The distance between two points is found using the formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2).

Here, (x1, y1) and (x2, y2) are the coordinates of the two points, and d is the distance.

Calculating the Distance:



Subtract the x and y coordinates of the two points, square these differences, add them, and take the square root.

The formula is based on the Pythagorean theorem.

Example:



Finding the Distance Between Two Points:



To calculate the distance between points (3, 4) and (6, 8):

d = sqrt((6 - 3)^2 + (8 - 4)^2) = sqrt(9 + 16) = sqrt(25) = 5 units.

The distance is 5 units.

Checking the Calculation:



Ensure correct subtraction of coordinates and accurate squaring of differences.

Confirm the square root calculation.

Key Points to Remember:



This formula is a practical use of the Pythagorean theorem in coordinates.

The distance is always a positive number.

Activity:



Practice this calculation with various point pairs.

Plot the points on graph paper to visualize the distance.

Extra Tip:



This concept is key for spatial understanding and is used in fields like physics, engineering, and computer science.