Vector AB is a vector whose tail is at (-4,2) and whose head is at (-1,3).

Calculate the magnitude of vector AB
Determine the coordinates of point D on vector CD, if C (-6,0) and vector CD= vector AB.

Please I need some help. Is there a formula to solve this? Pls help

I will let A be (-4,2) and B(-1,3)

vector AB = ( -1+4 , 3-2)
= (3,1)
magnitude of AB = √(3^2 + 1^2) = √10

let D be (x,y)
the vector CD = (x+6, x-0) = (x+6 , y)
but if vector AB = vector CD
then x+6 = 3
x = -3
and y = 1
so point D is (-3,1)

in general if A is the point (a,b) and B is the point (c,d)
then vector AB = ( c-a , d-b)
and vector BA = ( a - c, b - d)

note that vector AB = - vector BA

Very well explained thank you.

Oh, I'm happy to help you out! Don't worry, there are formulas to solve these problems.

To calculate the magnitude of vector AB, you can use the distance formula. The formula is:

Magnitude = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, the coordinates of the tail of vector AB are (-4,2) and the coordinates of the head are (-1,3). So, plugging in the values into the formula, we get:

Magnitude = √((-1 - (-4))^2 + (3 - 2)^2)
= √(3^2 + 1^2)
= √(9 + 1)
= √10

Therefore, the magnitude of vector AB is √10.

Now, let's move on to finding the coordinates of point D on vector CD. Since vector CD is equal to vector AB, the coordinates of point D will be the same as the coordinates of the head of vector AB, which is (-1,3).

So, the coordinates of point D are (-1,3).

I hope that helps! Let me know if you have any other questions, or if you need another dose of humor.

Yes, there are formulas to solve this. To calculate the magnitude of vector AB, you can use the formula:

Magnitude of AB = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) represent the coordinates of the starting point (tail) of vector AB, and (x2, y2) represent the coordinates of the end point (head) of vector AB.

In this case, the starting point of vector AB is (-4, 2), and the end point is (-1, 3). So, applying the formula:

Magnitude of AB = sqrt((-1 - (-4))^2 + (3 - 2)^2)
= sqrt(3^2 + 1^2)
= sqrt(9 + 1)
= sqrt(10)

So, the magnitude of vector AB is sqrt(10).

To find the coordinates of point D on vector CD, if C is (-6, 0) and vector CD equals vector AB, you can use the formula:

Coordinates of D = (x2 + xC - x1, y2 + yC - y1)

where (x1, y1) represent the coordinates of the starting point (tail) of vector CD (point C), (x2, y2) represent the coordinates of the end point (head) of vector CD (point D), and (xC, yC) represent the coordinates of point C.

In this case, (xC, yC) = (-6, 0), (x1, y1) = (-4, 2), and (x2, y2) represent the coordinates we're trying to find.

Plugging in the values:

(x2, y2) = (-1 + (-6) - (-4), 3 + 0 - 2)
= (-1 -6 + 4, 3 - 2)
= (-7 + 4, 1)
= (-3, 1)

Thus, the coordinates of point D on vector CD are (-3, 1).

Yes, there are formulas to calculate the magnitude of a vector and determine the coordinates of a point on a vector. I'll explain the steps to solve each part of your question.

1. Calculating the magnitude of vector AB:
To find the magnitude of a vector, you can use the formula:

|AB| = √((x2 - x1)^2 + (y2 - y1)^2)

Where (x1, y1) represents the coordinates of the tail of the vector, and (x2, y2) represents the coordinates of the head of the vector.

In this case, the tail of vector AB is given as (-4, 2), and the head is given as (-1, 3).

Substituting these values into the formula, we get:

|AB| = √((-1 - (-4))^2 + (3 - 2)^2)
= √((3)^2 + (1)^2)
= √(9 + 1)
= √10

Therefore, the magnitude of vector AB is √10.

2. Determining the coordinates of point D on vector CD:
Since vector CD is equal to vector AB, the coordinates of D will be the same as the coordinates of B. Thus, D will also have coordinates (-1, 3).

I hope this helps! Let me know if you have any further questions or need additional clarifications.