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Mathematics

Find the ratio in which the join of (-4, 7) and (3, 0) is divided by the y-axis. Also, find the co-ordinates of the point of intersection.

Section Formula

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Answer

Let the point on y-axis be (0, y) and required ratio be k : 1.

By formula,

x=m1x2+m2x1m1+m2x = \dfrac{m1x2 + m2x1}{m1 + m2}

Substituting values we get,

0=k×3+1×4k+10=3k43k=4k=43.\Rightarrow 0 = \dfrac{k \times 3 + 1 \times -4}{k + 1} \\[1em] \Rightarrow 0 = 3k - 4 \\[1em] \Rightarrow 3k = 4 \\[1em] \Rightarrow k = \dfrac{4}{3}.

k : 1 = 43:1=4:3\dfrac{4}{3} : 1 = 4 : 3.

y=m1y2+m2y1m1+m2y = \dfrac{m1y2 + m2y1}{m1 + m2}

Substituting values we get,

y=4×0+3×74+3y=0+217y=3.\Rightarrow y = \dfrac{4 \times 0 + 3 \times 7}{4 + 3} \\[1em] \Rightarrow y = \dfrac{0 + 21}{7} \\[1em] \Rightarrow y = 3.

P = (0, y) = (0, 3).

Hence, ratio = 4 : 3 and co-ordinates of point of intersection = (0, 3).

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