Final answer:
The magnitude of a vector starting at (3, 4) and ending at (10, 3) is calculated using the distance formula, resulting in a magnitude of approximately 7.07 units.
Step-by-step explanation:
To find the magnitude of a vector that starts at point (3, 4) and ends at point (10, 3), we can use the distance formula. The magnitude of a vector is the length of the vector, which is calculated by taking the square root of the sum of the squares of its components. Here are the steps to calculate the magnitude:
- Find the change in x (x-component): 10 - 3 = 7
- Find the change in y (y-component): 3 - 4 = -1
- Apply the Pythagorean theorem to find the magnitude: √(7^2 + (-1)^2) = √(49 + 1) = √50
- Calculate the square root to two decimal places: √50 ≈ 7.07
The magnitude of the vector is 7.07 units (to two decimal places).