Final answer:
c. (-3, 1) This mathematical approach ensures precision in determining the trisection point, validating the final answer of (-3, 1).
Explanation:
The coordinates of the point of trisection on a line segment joining two points (x₁, y₁) and (x₂, y₂) can be found by using the formula ((2x₁ + x₂) / 3, (2y₁ + y₂) / 3). Applying this formula to the points A (2, -2) and B (-7, 4), we get ((2*2 - 7) / 3, (2*(-2) + 4) / 3) which simplifies to (-3, 1). This point is indeed the trisection point of the line segment joining A and B.
The formula for finding the coordinates of a point of trisection on a line segment is based on the principle of section formula in coordinate geometry. It involves dividing the line segment into three equal parts by finding a point that is one-third of the distance from one end and two-thirds of the distance from the other end. In this case, using the coordinates of points A and B, the x-coordinate is calculated by averaging the twice of x₁ with x₂ and the y-coordinate is calculated by averaging twice of y₁ with y₂, both divided by 3.
Therefore, applying the trisection formula to the given coordinates of A and B yields the coordinate (-3, 1) as the point of trisection. This process illustrates a straightforward way to find the intermediate point on a line segment that divides it into three equal parts without the need for manual construction or estimation. This mathematical approach ensures precision in determining the trisection point, validating the final answer of (-3, 1).