Vector vec(u) has an initial point (4,8) and a terminal point (2,4). Find the magnitude of vec(u). Enter an exact answer as an expression with a square root symbol or enter an approximate answer as a decimal rounded to the nearest hundredth. || vec(u)||=◻

Question

Vector  vec(u) has an initial point  (4,8) and a terminal point  (2,4). Find the magnitude of  vec(u). Enter an exact answer as an expression with a square root symbol or enter an approximate answer as a decimal rounded to the nearest hundredth.  || vec(u)||=◻

Bytelearn · Accepted Answer

Calculate Differences: To find the magnitude of the vector vec(u), we need to use the distance formula, which is derived from the Pythagorean theorem. The magnitude of a vector with initial point (x1, y1) and terminal point (x2, y2) is given by the square root of the sum of the squares of the differences in the x-coordinates and y-coordinates.Square Differences: First, we calculate the differences in the x-coordinates and y-coordinates. For vec(u), the initial point is (4,8) and the terminal point is (2,4). So, the difference in the x-coordinates is 2 - 4 = -2, and the difference in the y-coordinates is 4 - 8 = -4.Add Squares: Next, we square the differences we found in the previous step. (-2)^2 = 4 and (-4)^2 = 16.Find Magnitude: Now, we add the squares of the differences to find the sum: 4 + 16 = 20.Finally, we take the square root of the sum to find the magnitude of vec(u). The square root of 20 is √20, which can be simplified to 2√5. If we want a decimal approximation, we calculate √20 ≈ 4.47 (rounded to the nearest hundredth).

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