Final answer:
The magnitude of vector AB, given points A = (-6, 8) and B = (10,6), is calculated using the distance formula and results in approximately 16.12 units.
Step-by-step explanation:
The student's question refers to finding the magnitude of the vector AB, which can be interpreted as the displacement from point A to point B or the distance between two points in a coordinate plane. To find the magnitude of AB, we calculate it using the distance formula which is derived from the Pythagorean theorem.
To start, let A = (-6, 8) and B = (10,6). The distance between A and B (the magnitude of vector AB) can be found using the distance formula:
AB = √[(x2 - x1)^2 + (y2 - y1)^2]
Substituting the coordinates of points A and B gives:
AB = √[(10 - (-6))^2 + (6 - 8)^2]
AB = √[(16)^2 + (-2)^2]
AB = √[256 + 4]
AB = √[260]
AB = ≈16.12
Thus, the magnitude of vector AB is approximately 16.12 units.