What is the magnitude of the vector with an initial point (2,1) and terminal point (-13,9)? Answers-7.9,12.7,17.0,23.0
It's the same as calculating the distance between two points.
||A||= sqrt((-13-2)²+(9-1)²)
=17
Well, let's put this in perspective. You've got a vector that's feeling a bit lost, wandering around from (2,1) to (-13,9). Poor vector! But let's not get too caught up in its existential crisis. The magnitude of this vector can be determined by its length, which we can find using the good ol' distance formula.
So, let's go on a journey to calculate this magnitude. The distance formula says that the magnitude of a vector with initial point (x1, y1) and terminal point (x2, y2) is given by the square root of [(x2 - x1)^2 + (y2 - y1)^2].
Plugging in the values, we get sqrt[(-13 - 2)^2 + (9 - 1)^2]. Simplifying that, we get sqrt[(-15)^2 + (8)^2]. Whoops, it seems we've made a little mistake there. (-15)^2 is 225, not -15. My bad!
So, let's try again. We have sqrt[(225) + (64)]. Adding those together, we get sqrt[289]. And what's the square root of 289? It's 17.
So, after all that wandering and confusion, the magnitude of this vector is 17.0.
To find the magnitude of a vector, we use the distance formula in two dimensions. The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the initial point is (2,1) and the terminal point is (-13,9). Using these values in the distance formula, we have:
d = √((-13 - 2)^2 + (9 - 1)^2)
= √((-15)^2 + (8)^2)
= √(225 + 64)
= √289
= 17.0
Therefore, the magnitude of the vector is 17.0.
To find the magnitude of a vector, you can use the distance formula. Here are the steps to determine the magnitude of the vector with an initial point (2,1) and terminal point (-13,9):
Step 1: Find the difference between the x-coordinates of the initial and terminal points. For this vector, it is (-13 - 2) = -15.
Step 2: Find the difference between the y-coordinates of the initial and terminal points. In this case, it is (9 - 1) = 8.
Step 3: Square both the x and y differences. (-15)^2 = 225 and 8^2 = 64.
Step 4: Add the squared x and y differences together. 225 + 64 = 289.
Step 5: Take the square root of the sum from step 4. √289 = 17.
Therefore, the magnitude of the vector is 17.0 according to the given options.