Question

Given points A(9, 3), B(–3, 6), and C(–7, –3). Which statements describe the vectors that include these points? Check all that apply.

-The magnitude of Vector A C is StartRoot 2 EndRoot.
-The magnitude of Vector B C is StartRoot 97 EndRoot.
-The magnitude of Vector A B is 3 StartRoot 17 EndRoot.
-Vector A C = LeftAngleBracket negative 16, negative 6 RightAngleBracket
-Vector B C = LeftAngleBracket 10, 9 RightAngleBracket
-Vector A B = LeftAngleBracket negative 12, 3 RightAngleBracket

Answer 1

The statements that describe the vectors that include points A(9,3), B(-3,6), and C(-7,-3) are: The magnitude of Vector AC is sqrt(2), the magnitude of Vector BC is sqrt(97), and the magnitude of Vector AB is 3*sqrt(17).

Step-by-step explanation:

To determine which statements describe the vectors that include points A(9,3), B(-3,6), and C(-7,-3), we can calculate the magnitudes and directions of each vector.

1. Magnitude of Vector AC: We can use the distance formula to find the distance between points A and C, which is equal to sqrt((9-(-7))^2 + (3-(-3))^2). This is equal to sqrt(2).
2. Magnitude of Vector BC: We can use the distance formula to find the distance between points B and C, which is equal to sqrt((-3-(-7))^2 + (6-(-3))^2). This is equal to sqrt(97).
3. Magnitude of Vector AB: We can use the distance formula to find the distance between points A and B, which is equal to sqrt((9-(-3))^2 + (3-6)^2). This is equal to 3*sqrt(17).
4. Vector AC: We can find the vector AC by subtracting the coordinates of point A from the coordinates of point C. This gives us AC = <-16, -6>.
5. Vector BC: We can find the vector BC by subtracting the coordinates of point B from the coordinates of point C. This gives us BC = <10, 9>.
6. Vector AB: We can find the vector AB by subtracting the coordinates of point A from the coordinates of point B. This gives us AB = <-12, 3>.

Answer 2

Answer: William is right 2, 3, 4, and 6

Step-by-step explanation: