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Question
Find the coordinates of the points of trisection of the line segment joining (4, -1) and (-2, -3).
Solution
Let P (x1, y1) and Q (x2, y2) are the points of trisection of the line segment joining the given points i.e., AP = PQ = QB
Therefore, point P divides AB internally in the ratio 1:2.
∴ `x = (m_1x_2 + m_2x_1)/(m_1 + m_2),` `y = (m_1y_2 + m_2y_1)/(m_1 + m_2)`
`x_1= (1xx(-2)+2xx4)/(1+2), y_1 = (1xx(-3)+2xx(-1))/(1+2)`
`x_1 = (-2+8)/3=6/3=2, y_1 = (-3-2)/3 = (-5)/3`
Therefore, P(x1, y1) = `(2, -5/3)`
Point Q divides AB internally in the ratio 2:1.
∴ `x = (m_1x_2 + m_2x_1)/(m_1 + m_2),` `y = (m_1y_2 + m_2y_1)/(m_1 + m_2)`
`x_2=(2xx(-2)+1xx4)/(2+1), y_2=(2xx(-3)+1xx(-1))/(2+1)`
`x_2 = (-4+4)/3 = 0, y_2= (-6-1)/3 = (-7)/3`
`Q(x_2, y_2) = (0, -7/3)`
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