Find the coordinates of the points of trisection of the line segment joining the points A(2, -2) and B(-7, 4).

Step 1: Understand Trisection

Trisection means dividing a line segment into three equal parts. If P and Q are the points of trisection, then P divides the segment AB in the ratio $1:2$, and Q divides the segment AB in the ratio $2:1.

Step 2: Apply Section Formula for Point P

We use the section formula to find the coordinates of point P. Here, $(x_1, y_1) = (2, -2)$, $(x_2, y_2) = (-7, 4)$, and the ratio $(m_1:m_2) = (1:2)$. Substituting these values, we find the coordinates of P.

Step 3: Apply Section Formula for Point Q

Next, we find the coordinates of point Q using the section formula. For Q, the ratio $(m_1:m_2) = (2:1)$. We substitute the coordinates of A and B and the new ratio into the formula to find the coordinates of Q.

More from this chapter

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