Question

Find the radio in which the line segment joining the points(3,4) and (-34) is divided internally by the y-axis

Answer 1

COMPLETE QUESTION-

Find the ratio in which the line segment joining the points (3,4) and (-3,4) is divided internally by y-axis.

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore Ratio=1:1}}$

${\bold{\underline{\underline{Step-by-stel\:explanation:}}}}$

$\underline \bold{Given : } \\ \implies First\: end\: point = (3.4) \\ \\ \implies Second \: end \: point = ( - 3.4) \\ \\ \underline \bold{To \: Find: } \\ \implies Ratio = ?$

• According to given question :

$\bold{Let \: p \: be \: the \: point \: on \: y \: axis \: with } \\ \bold{ point = (0.4)} \\ \\ \bold{Let \: Ratio \: = k : 1} \\ \\ \bold{Using \: section \: formula : }\\ \implies x = \frac{m x_{2} + nx_{1} }{2} \\ \\ \implies 0 = \frac{k \times ( - 3) + 1 \times 3}{2} \\ \\ \implies - 3k + 3 = 0 \\ \\ \implies - 3k = - 3 \\ \\ \bold{\implies k = 1} \\ \\ \bold{For \: y : }\\ \implies y = \frac{m y_{2} + n y_{1} }{2} \\ \\ \implies 4 = \frac{k \times 4 + 1 \times 4}{2} \\ \\ \implies 4 \times 2 = 4k + 4 \\ \\ \implies 8 - 4 = 4k \\ \\ \implies 4k = 4 \\ \\ \implies k = \frac{4}{4} \\ \\ \bold{\implies k = 1}\\ \\ \bold{\therefore Ratio = 1 : 1}$

Answer 2

$\bold{let \: ratio \: = k : 1} \\ \\ \bold{using \: section \: formula : }\\ \to x = \frac{m x_{2} + nx_{1} }{2} \\ \\ \to 0 = \frac{k \times ( - 3) + 1 \times 3}{2} \\ \\ \to - 3k + 3 = 0 \\ \\ \to - 3k = - 3 \\ \\ \bold{\to k = 1} \\ \\ \bold{for \: y : }\\ \to y = \frac{m y_{2} + n y_{1} }{2} \\ \\ \to 4 = \frac{k \times 4 + 1 \times 4}{2} \\ \\ \to 4 \times 2 = 4k + 4 \\ \\ \to 8 - 4 = 4k \\ \\ \to 4k = 4 \\ \\ \to k = \frac{4}{4} \\ \\ \bold{\to k = 1}\\ \\ \bold{\therefore ratio = 1 : 1}$