How do you calculate the distance between the points (1, 4) and (6, 2)?

To calculate the distance between the points (1, 4) and (6, 2), we use the distance formula derived from the Pythagorean theorem. The formula for the distance (
d) between two points (x₁, y₁) and (x₂, y₂) in a 2D plane is:

d = √((x₂ – x₁)² + (y₂ – y₁)²)

Substituting our points into the formula, we have:

• x₁ = 1, y₁ = 4
• x₂ = 6, y₂ = 2

d = √((6 – 1)² + (2 – 4)²)

Calculating the differences:

• (6 – 1) = 5
• (2 – 4) = -2

Now square these differences:

• 5² = 25
• (-2)² = 4

Now, sum these squares:

Finally, take the square root of this sum:

The exact distance between the points (1, 4) and (6, 2) is thus
√29, which is approximately 5.39 when calculated to two decimal places.