Find the magnitude of the vector in standard position with end point (5, -2).
A)4.6
B)6.4
C)1.5
D)5.4

Question

Quizplus · Accepted Answer

To find the magnitude of the vector, we need to use the distance formula in reverse. Starting from the origin (0,0), we can create a right triangle with the given end point (5,-2) as the hypotenuse. Drawing this out, we can see that the horizontal leg has a length of 5 and the vertical leg has a length of 2.

Using the Pythagorean theorem, we can solve for the length of the hypotenuse (which represents the magnitude of the vector):

c^2 = a^2 + b^2
c^2 = 5^2 + 2^2
c^2 = 25 + 4
c^2 = 29
c = sqrt(29)

Therefore, the magnitude of the vector is approximately 5.4. The correct answer is D.

Find the Magnitude of the Vector in Standard Position with End