Final answer:
To find the coordinates of point 'b', find the point that is 2/3 of the distance from point 'a' to point 'c'. The coordinates of point 'b' are (8, -4).
Step-by-step explanation:
To find the coordinates of point 'b', we need to find the point that is 2/3 of the distance from point 'a' to point 'c'.
First, we need to find the difference between the x-coordinates and y-coordinates of points 'a' and 'c':
Δx = 11 - 2 = 9
Δy = -3 - (-6) = 3
Next, we multiply the difference by 2/3:
(2/3)Δx = (2/3) * 9 = 6
(2/3)Δy = (2/3) * 3 = 2
Finally, we add the result to the x-coordinate of point 'a' and the y-coordinate of point 'a' to get the coordinates of point 'b':
x-coordinate of 'b': 2 + 6 = 8
y-coordinate of 'b': -6 + 2 = -4
Therefore, the coordinates of point 'b' are (8, -4).