Final answer:
The magnitude of vector h with an initial point at (8.2, 9.6) and a terminal point at (4.3, -2.7) is approximately 12.903 when rounded to the nearest thousandth.
Step-by-step explanation:
To find the magnitude of the vector h with an initial point at (8.2, 9.6) and a terminal point at (4.3, -2.7), we can use the distance formula derived from the Pythagorean Theorem. The formula for finding the magnitude of a vector (|h|) when given its initial and terminal points is |h| = √((x2 - x1)² + (y2 - y1)²), where (x1, y1) is the initial point and (x2, y2) is the terminal point.
We calculate this as follows:
|h| = √((4.3 - 8.2)² + (-2.7 - 9.6)²)
|h| = √((-3.9)² + (-12.3)²)
|h| = √(15.21 + 151.29)
|h| = √(166.5)
Therefore, the magnitude of vector h, rounded to the nearest thousandth, is approximately 12.903.