Point B (5,2) is located on AC such as that AB is ¼ of AC. Find the coordinates of point C if point A is located at (7,4).
After graphing the points provided, what would my next step?
B-A = (-2,-2)
So C-B = 3(B-A) = (-6,-6)
C = B+(-6,-6) = (-1,-4)
well C is to the left and down
B is down 2 from A (4-2 = 2)
so
C is down 4*2 = 8 from A
so y coordinate of C is 4 - 8 = -4
and B is left 7-5 = 2 from A
so
C is left 4*2 = 8 from A
so x coordinate of C is 7 - 8 = -1
so C is at ( -1 , -4 )
After graphing the points A (7,4) and B (5,2), you can find the coordinates of point C by following these steps:
Step 1: Determine the vector from A to B.
To find the vector from point A to point B, subtract the x-coordinates and y-coordinates of B from the corresponding coordinates of A:
Vector AB = (5-7, 2-4) = (-2, -2)
Step 2: Determine the vector from A to C.
Since AB is 1/4 of AC, the vector AC will be four times the vector AB. Multiply the x-coordinate and y-coordinate of AB by 4:
Vector AC = 4 * Vector AB = 4 * (-2, -2) = (-8, -8)
Step 3: Add the vector AC to the coordinates of A.
To get the coordinates of point C, add the x-coordinate and y-coordinate of AC to the corresponding coordinates of A:
C = (7 + (-8), 4 + (-8)) = (-1, -4)
Therefore, the coordinates of point C are (-1, -4).