Question

Find the distance between the pair of points (2,5) and (6,9). If necessary, express the answer in simplified radical form and then round to two decimal places.

Answer 1

The distance between the pair of points (2,5) and (6,9) is approximately 5.66 units.

Step-by-step explanation:

To find the distance between two points in a coordinate plane, we can use the distance formula. The distance formula is derived from the Pythagorean theorem and is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using the coordinates (2,5) and (6,9), we can plug in the values into the formula:

d = sqrt((6 - 2)^2 + (9 - 5)^2) = sqrt(16 + 16) = sqrt(32) ≈ 5.66

So, the distance between the pair of points (2,5) and (6,9) is approximately 5.66 units.

Distance can refer to the amount of space between two points or objects. It's often measured in units like meters, kilometers, miles, etc., depending on the context. In a broader sense, it can also represent a gap or emotional space between people or ideas.