To calculate the distance between two points on a coordinate grid, we can use the distance formula. The distance formula is derived from the Pythagorean theorem and is given by:
d = √[(x₂ – x₁)² + (y₂ – y₁)²]
Here, (x₁, y₁) and (x₂, y₂) are the coordinates of the two points. In this case, the points are:
- Point 1: (7, 8) – where x₁ = 7 and y₁ = 8
- Point 2: (8, 0) – where x₂ = 8 and y₂ = 0
Now, we can plug these values into the distance formula:
d = √[(8 - 7)² + (0 - 8)²]Breaking it down step-by-step:
- Calculate the difference in x-coordinates: (8 – 7) = 1.
- Calculate the difference in y-coordinates: (0 – 8) = -8.
- Now square both results: (1)² = 1 and (-8)² = 64.
- Add those squares together: 1 + 64 = 65.
- Finally, take the square root of that sum: √65 ≈ 8.06.
Therefore, the distance between the points (7, 8) and (8, 0) on a coordinate grid is approximately 8.06 units.