The line segment joining the points (3, -4) and (1, 2) is trisected. Find the coordinates of the point of trisection closer to (3, -4).
Answer: A
The points of trisection divide the line segment into three equal parts. The point closer to A(3, -4) will divide the segment AB in the ratio 1:2.
Let A=(3,-4) and B=(1,2). The ratio is \(m_1:m_2 = 1:2\).
x = \(\frac{1(1) + 2(3)}{1+2} = \frac{1+6}{3} = \frac{7}{3}\)
y = \(\frac{1(2) + 2(-4)}{1+2} = \frac{2-8}{3} = \frac{-6}{3} = -2\)
The coordinates are (7/3, -2).