To find the coordinates of vector AB given the coordinates of points A and B, we can follow a straightforward formula. Let's break it down step-by-step.
Understanding Points A and B
- Point A has coordinates (3, 7)
- Point B has coordinates (-1, 4)
Vector AB Definition
- Vector AB is defined as the difference between the coordinates of point B and point A.
Formula to Find Vector AB
- The formula to calculate vector AB is:
AB = B - A
Calculating the Coordinates
- To find the x-coordinate of vector AB:
- x-coordinate of AB = x-coordinate of B - x-coordinate of A
- x-coordinate of AB = -1 - 3 = -4
- To find the y-coordinate of vector AB:
- y-coordinate of AB = y-coordinate of B - y-coordinate of A
- y-coordinate of AB = 4 - 7 = -3
Final Coordinates of Vector AB
- Therefore, the coordinates of vector AB are:
- AB = (-4, -3)
Summary
- Vector AB represents the directional change from point A to point B.
- The calculated coordinates indicate that moving from A to B involves a movement of -4 units in the x-direction and -3 units in the y-direction.
By following these steps, you can clearly understand how to find the coordinates of vector AB using the coordinates of points A and B.