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Example 9 Find the ratio in which the y−axis divides the line segment joining the points (5, – 6) and (–1, – 4). Also find the point of intersection. Let the point be A(5, −6) & B(−1, −4) Let Point P the required required point Since Point P is on y−axis, hence its x coordinate is 0. So, it is of the form P(0, y) Now, we have to find ratio Let ratio be k : 1 Hence, m1 = k, m2 = 1 x1 = 5, y1 = −6 x2 = −1, y2 = −4 x = 0, y = y Using section formula x = (𝑚_1 𝑥_2 + 𝑚_2 𝑥_1)/(𝑚_1+ 𝑚_2 ) 0 = (𝑘 ×−1 + 1 × 5)/(𝑘 + 1) 0 = (−𝑘 + 5)/(𝑘 + 1) 0(k + 1) = −k + 5 0 = −k + 5 k = 5 Hence, k = 5 Now, we need to find y also y = (𝑚_1 𝑦_2 + 𝑚_2 𝑦_1)/(𝑚_1 + 𝑚_2 ) = (𝑘 × −4 + 1 × −6)/(𝑘 + 1) = (5 × −4 + 1 × 1)/(5 + 1) = (−20 − 6)/6 = (−26)/6 = (−13)/3 Hence the coordinate of point is P(0, y) = P ("0, " (−𝟏𝟑)/𝟑)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.