Ex 7.2, 2 - Find coordinates of points of trisection - Ex 7.2

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Ex 7.2 , 2 Find the coordinates of the points of trisection of the line segment joining (4, –1) and (–2, –3). Let the given points be A(4, −1) & B(−2, 3) P & Q are two points on AB such that AP = PQ = QB Let AP = PQ = QB = m Point P divides AP & PB in the ratio AP = m PB = PQ + QB = k + k = 2k Hence, Ratio between AP & PB = AP/PB = 𝑘/2𝑘 = 1/2 Thus P divides AB in the ratio 1:2 Finding P Let P(x, y) m1 = 1 , m2 = 2 And for AB x1 = 4 , x2 = −2 y1 = −1 , y2 = −3 Hence, point P is P(x, y) = P(2, (−5)/3) Similarly, Point Q divides AB in the ratio AQ & QB 𝐴𝑄/𝑄𝐵 = (𝐴𝑃 + 𝑃𝑄)/𝑄𝐵 = (𝑘 + 𝑘 )/𝑘 = 2𝑘/𝑘 = 2/1 = 2 : 1 Finding Q Let Q be Q(x , y) m1 = 2 , m2 = 1 x1 = 4 , x2 = −2 y1 = −1 , y2 = −3 Hence, point Q is Q(x, y) = Q(0, (−7)/3)

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