The two possible locations of the point C are (1, 1) and (- 2, - 5).
How to determine the two location of a point within a line based on a given ratio
According to the statement, we find the coordinates of the ends of a line segment and a partition ratio. There are two possible solutions concening the location of the point B:
- AC / BC = 4 : 1
- BC / AC = 4 : 1
Thus, we have the corresponding expressions for each case:
Case 1
C(x, y) = A(x, y) + (4 / 5) · [B(x, y) - A(x, y)]
C(x, y) = (- 3, - 7) + (4 / 5) · [(2, 3) - (- 3, - 7)]
C(x, y) = (- 3, - 7) + (4 / 5) · (5, 10)
C(x, y) = (- 3, - 7) + (4, 8)
C(x, y) = (1, 1)
Case 2
C(x, y) = A(x, y) + (1 / 5) · [B(x, y) - A(x, y)]
C(x, y) = (- 3, - 7) + (1 / 5) · [(2, 3) - (- 3, - 7)]
C(x, y) = (- 3, - 7) + (1 / 5) · (5, 10)
C(x, y) = (- 3, - 7) + (1, 2)
C(x, y) = (- 2, - 5)
The two possible locations of the point C are (1, 1) and (- 2, - 5).
To learn more on partition ratios: https://brainly.com/question/3148758
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