Final answer:
The distance between the two points (-5, 2) and (6,8) is calculated using the distance formula, with a final result of approximately 12.53 units when rounded to the nearest hundredth.
Step-by-step explanation:
The student asks for the calculation of the distance between two given points, which can be found using the distance formula. The distance formula for two-dimensional space is D = √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points. Plugging in the coordinates of the points given by the student, (-5, 2) and (6,8), we get:
D = √((6 - (-5))^2 + (8 - 2)^2)
D = √((6 + 5)^2 + (6)^2)
D = √(11^2 + 6^2)
D = √(121 + 36)
D = √157
Upon calculating the square root of 157 and rounding to the nearest hundredth, we find:
D ≈ 12.53
Therefore, the distance between the two points is approximately 12.53 units.