Final answer:
The point that divides AB two-thirds of the way from A to B is (-2/3, 1/3).
Step-by-step explanation:
To find the point that divides AB two-thirds of the way from A to B, we can use the section formula. The section formula states that the coordinates of the point dividing a line segment with endpoints (x1, y1) and (x2, y2) into two parts with ratios m:n are given by:
x = (m*x2 + n*x1) / (m + n)
y = (m*y2 + n*y1) / (m + n)
In this case, A has coordinates (4,1), B has coordinates (-3,0), and we want to divide AB two-thirds of the way from A to B, so m = 2 and n = 1. Plugging in these values, we get:
x = (2*-3 + 1*4) / (2 + 1) = -2/3
y = (2*0 + 1*1) / (2 + 1) = 1/3
Therefore, the point that divides AB two-thirds of the way from A to B is (-2/3, 1/3).