Final answer:
The distance between two points (x1, y1) and (x2, y2) on a coordinate plane is found using the distance formula derived from the Pythagorean theorem. A step-by-step method includes subtracting and squaring the coordinates' differences, summing these squares, and then taking the square root of this sum to get the distance, which represents the straight-line path between the points.
Step-by-step explanation:
When determining the distance between two points on a coordinate plane, you can employ the distance formula which is derived from the Pythagorean theorem. The formula states that the distance is the square root of the sum of the squares of differences in the x-coordinates and the y-coordinates of the two points, represented by distance = √((x2 - x1)² + (y2 - y1)²). It is important to first assign which direction will be positive. This helps in ensuring that the values subtracted within the distance formula maintain consistency in terms of direction.
Here is a step-by-step explanation using the formula to find the distance between point (x1, y1) and point (x2, y2):
- Subtract the x-coordinate of the first point from the x-coordinate of the second point to find (x2 - x1).
- Subtract the y-coordinate of the first point from the y-coordinate of the second point to find (y2 - y1).
- Square each of the differences obtained from steps 1 and 2, which gives you (x2 - x1)² and (y2 - y1)².
- Add the squared differences from step 3, obtaining (x2 - x1)² + (y2 - y1)².
- Take the square root of the sum from step 4 to find the distance, which is the length of the straight-line path between the two points.
Remember, distance traveled refers to the total length of the path traveled between two positions, while the distance we calculate here represents the magnitude of displacement, which is the straight-line distance between the initial and final positions, irrespective of the path taken.