Answer: Therefore, the coordinates of point B that partitions the segment AC such that AB:BC is 1:2 are (1.17, -2.17).
Explanation:
Let's first find the coordinates of the midpoint of AC, which will be the coordinates of point B if AB:BC is 1:2.
The x-coordinate of the midpoint = (x-coordinate of A + x-coordinate of C) / 2 = (-5 + 4) / 2 = -0.5
The y-coordinate of the midpoint = (y-coordinate of A + y-coordinate of C) / 2 = (4 - 5) / 2 = -0.5
So the midpoint of AC is B(-0.5, -0.5).
Now we can find the coordinates of A by using the midpoint formula:
The x-coordinate of A = (2 * x-coordinate of B + x-coordinate of C) / 3 = (2 * (-0.5) + 4) / 3 = 1.17
The y-coordinate of A = (2 * y-coordinate of B + y-coordinate of C) / 3 = (2 * (-0.5) - 5) / 3 = -2.17
So the coordinates of point A are (1.17, -2.17).
Therefore, the coordinates of point B that partitions the segment AC such that AB:BC is 1:2 are (1.17, -2.17).