Question
Show Examples
What are the coordinates of the point on the directed line segment from $(-7,3)$ to $(4,-8)$ that partitions the segment into a ratio of 6 to 5 ?
Answer Attemptiout of 2

Step 1 ：We are given the coordinates of the endpoints of the line segment as $(-7,3)$ and $(4,-8)$, and the ratio as 6 to 5.

Step 2 ：We can use the formula for the division of a line segment in a given ratio to find the coordinates of the point that partitions the line segment. The formula is: \[ (x, y) = \left( \frac{m_1x_2 + m_2x_1}{m_1 + m_2}, \frac{m_1y_2 + m_2y_1}{m_1 + m_2} \right) \]

Step 3 ：Substituting the given values into the formula, we get: \[ x = \frac{6*4 + 5*(-7)}{6 + 5} = -1.0 \] and \[ y = \frac{6*(-8) + 5*3}{6 + 5} = -3.0 \]

Step 4 ：So, the coordinates of the point that partitions the line segment from $(-7,3)$ to $(4,-8)$ into a ratio of 6 to 5 are \(\boxed{(-1.0, -3.0)}\)