How do you calculate the distance between the points (6, 2) and (8, 10) on a coordinate grid?

To calculate the distance between two points on a coordinate grid, we use the distance formula, which is derived from the Pythagorean theorem. The distance formula is given by:

d = √((x₂ – x₁)² + (y₂ – y₁)²)

Here, (x₁, y₁) is the first point and (x₂, y₂) is the second point. In this case, our points are (6, 2) and (8, 10).

Let’s assign the coordinates:

• x₁ = 6
• y₁ = 2
• x₂ = 8
• y₂ = 10

Now, substitute these values into the distance formula:

d = √((8 – 6)² + (10 – 2)²)

Calculating the differences:

• (8 – 6) = 2
• (10 – 2) = 8

Now substitute these differences back into the formula:

d = √((2)² + (8)²)

Calculating the squares:

• (2)² = 4
• (8)² = 64

Now, add those values together:

d = √(4 + 64)

Which simplifies to:

d = √(68)

To get the final distance, calculate the square root of 68. We can approximate it:

d ≈ 8.246

Therefore, the distance between the points (6, 2) and (8, 10) on the coordinate grid is approximately 8.25 units.