Find the ordered pair that represents the vector from A(-4.3,-0.9) to B(-2.8,0.2)? Then find the magnitude of AB.
A. (1.5,1.1); 3.46
B. (-7.1, -0.7); 7.13
C. (1.5, 1.1); 1.86
D.(-7.1, -1.1); 7.18
I got C, is this right?
To find the vector from A to B, we subtract the coordinates of A from the coordinates of B.
The vector from A(-4.3, -0.9) to B(-2.8, 0.2) is (Bx - Ax, By - Ay).
Bx - Ax = -2.8 - (-4.3) = -2.8 + 4.3 = 1.5
By - Ay = 0.2 - (-0.9) = 0.2 + 0.9 = 1.1
So, the ordered pair that represents the vector from A to B is (1.5, 1.1).
To find the magnitude of AB, we can use the distance formula:
Magnitude of AB = sqrt((Bx - Ax)^2 + (By - Ay)^2)
= sqrt((1.5)^2 + (1.1)^2)
= sqrt(2.25 + 1.21)
= sqrt(3.46)
≈ 1.86
Therefore, the correct answer is:
C. (1.5, 1.1); 1.86
To find the vector from point A to point B, we need to subtract the coordinates of point A from the coordinates of point B.
So, let's subtract the x-coordinates and the y-coordinates separately:
x-coordinate of B - x-coordinate of A = -2.8 - (-4.3) = -2.8 + 4.3 = 1.5
y-coordinate of B - y-coordinate of A = 0.2 - (-0.9) = 0.2 + 0.9 = 1.1
Therefore, the ordered pair representing the vector from A to B is (1.5, 1.1).
Next, to find the magnitude of the vector AB, we use the formula for the magnitude of a vector. The magnitude of a vector (x, y) is given by the formula:
Magnitude = sqrt(x^2 + y^2)
Using the coordinates we found earlier, the magnitude of AB is:
Magnitude = sqrt(1.5^2 + 1.1^2) = sqrt(2.25 + 1.21) = sqrt(3.46)
So, the magnitude of AB is approximately 1.86.
Therefore, the correct answer is not C, but the correct answer is A. (1.5, 1.1); 3.46.
-2.8 - (-4.3) = 1.5
0.2 -(-0.9) = 1.1 so A or C so far
sqrt (1.5^2 + 1.1^2) = 1.86 so C