Find the coordinates of the point which divides the line segment joining (-1, 7) and (4, -3) in the ratio 2:3.
Answer: A
Using the section formula, the coordinates (x, y) are given by:
x = \(\frac{m_1x_2 + m_2x_1}{m_1+m_2}\) and y = \(\frac{m_1y_2 + m_2y_1}{m_1+m_2}\)
Here, \((x_1, y_1) = (-1, 7)\), \((x_2, y_2) = (4, -3)\), and \(m_1:m_2 = 2:3\).
x = \(\frac{2(4) + 3(-1)}{2+3} = \frac{8-3}{5} = \frac{5}{5} = 1\)
y = \(\frac{2(-3) + 3(7)}{2+3} = \frac{-6+21}{5} = \frac{15}{5} = 3\)
The coordinates are (1, 3).