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| 1. |
Find the coordinates of the points of trisection of the line sement joining (4,-1) and (-2,-3) |
| Answer» Let A(4,-1) and B(-2,-3) be the given points.Let P(x,y) and Q(a,b) be the points of\xa0trisection of AB so that AP = PQ = QBHence P divides AB internally in the\xa0ratio 1 : 2 and Q divides AB internally\xa0in the ratio 2 : 1By the section formula, the required points areAP = 1PQ = 1QB = 1Section formula internally = (lx₂ + mx₁)/(l + m) , (ly₂ + my₁)/(l + m)P divides the line segment in the ratio 1:2l = 1 m = 2 A(4,-1) and B(-2,-3) = [(1(-2) + 2(4)]/(1+2) , [(1(-3) + 2(-1)]/(1+2) = (-2+8)/3 , (-3-2)/3 = 6/3 , -5/3 = P (2 , -5/3)Q divides the line segment in the ratio 2:1l = 2 m = 1 = [(2(-2) + 1(4)]/(2+1) , [(2(-3) + 1(-1)]/(2+1) = (-4+4)/3 , (-6-1)/3 = 0/3 , -7/3 = Q (0 , -7/3)\xa0 | |