Final answer:
To find the distance between the points P_1=(0,0) and P_2=(6,1), the distance formula √((x_2 - x_1)^2 + (y_2 - y_1)^2) is used resulting in the exact distance of √37 or approximately 6.08 units.
Step-by-step explanation:
The distance d(P_1, P_2) between two points P_1 and P_2 in a coordinate plane can be found using the distance formula: d = √((x_2 - x_1)^2 + (y_2 - y_1)^2).
For the points P_1=(0,0) and P_2=(6,1), we substitute these values into the formula:
d = √((6 - 0)^2 + (1 - 0)^2)
= √(36 + 1)
= √37
The exact distance is √37 units, which is the square root of 37. If we require a decimal approximation, √37 is approximately 6.08 units.