Question

Find the magnitude of the vector PQ→ when P = (-1, 4) and Q = (7, 9). Round to the nearest hundredth.

A) 4.12
B) 5.39
C) 8.06
D) 10.82

Answer 1

The magnitude of vector PQ is approximately 9.43 when P = (-1, 4) and Q = (7, 9). This magnitude is calculated using the distance formula.

Step-by-step explanation:

To find the magnitude of the vector PQ→ when P = (-1, 4) and Q = (7, 9), we can use the distance formula, which is derived from the Pythagorean theorem, applied to vectors. The distance formula to calculate the magnitude of vector PQ is as follows:

1. First, calculate the difference in the x-coordinates of P and Q: (7 - (-1)) = 8.
2. Next, calculate the difference in the y-coordinates of P and Q: (9 - 4) = 5.
3. Then, plug these values into the distance formula: √((8)^2 + (5)^2).
4. Square the differences: 64 + 25 = 89.
5. Finally, take the square root of the sum: √89 ≈ 9.434, which we round to the nearest hundredth.

The magnitude of vector PQ→ is approximately 9.43, which rounds to 9.43 when rounded to the nearest hundredth. Therefore, the correct option is not listed among the options provided. Please check the options and the calculation for any possible errors.