1. In what ratio does the point T(x, 0) divide the segment joining the points S(5, 1) and U(-1, -2)?
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By: anil on 05 May 2019 01.46 am
Using section formula, the coordinates of point that divides line joining A = $$(x_1 , y_1)$$ and B = $$(x_2 , y_2)$$ in the ratio a : b = $$(frac{a x_2 + b x_1}{a + b} , frac{a y_2 + b y_1}{a + b})$$ Let the ratio in which the segment joining (5,1) and (-1,-2) divided by the x-axis = $$k$$ : $$1$$ Now, point P (x,0) divides (5,1) and (-1,-2) in ratio = k : 1 => $$0 = frac{(-2 imes k) + (1 imes 1)}{k + 1}$$ => $$-2k +1 = 0$$ => $$k = frac{-1}{-2} = frac{1}{2}$$ $$ herefore$$ Required ratio = 1 : 2 => Ans - (B)
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