Vector AB has initial point (4,3) and terminal point (-5,1) . Determine the coordinates of the terminal point of AC if AC= -2AB
The coordinates of vector AB are (4,3) -> (-5,1), which means the change in x is -5 - 4 = -9 and the change in y is 1 - 3 = -2.
Since AC = -2AB, the coordinates of vector AC will be -2 times the change in x and y of vector AB. So, the change in x for vector AC will be -2 * -9 = 18 and the change in y will be -2 * -2 = 4.
The initial point of AC is the same as the initial point of AB, which is (4,3). Therefore, to find the terminal point of AC, we need to add the change in x and y to the initial point:
x-coordinate of terminal point = 4 + 18 = 22
y-coordinate of terminal point = 3 + 4 = 7
Therefore, the terminal point of AC is (22,7).