1. In what ratio is the segment joining (-1,-12) and (3,4) divided by the x-axis?
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By: anil on 05 May 2019 02.10 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 (-1,-12) and (3,4) divided by the x-axis = $$k$$ : $$1$$ Since, the line segment is divided by x-axis, thus y coordinate of the point will be zero, let the point of intersection = $$(x,0)$$ Now, point P (x,0) divides (-1,-12) and (3,4) in ratio = k : 1 => $$0 = frac{(4 imes k) + (-12 imes 1)}{k + 1}$$ => $$4k - 12 = 0$$ => $$k = frac{12}{4} = 3$$ $$ herefore$$ Required ratio = 3 : 1 => Ans - (C)
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