Example 7 - Chapter 7 Class 10 Coordinate Geometry

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Example 7 In what ratio does the point ( 4, 6) divide the line segment joining the points A( 6, 10) and B(3, 8)? Given points A( 6, 10) & B(3, 8) Let point C( 4, 6) We need to find ratio between AC & CB Let the ratio be k : 1 Hence, m1 = k , m2 = 1 Also, x1 = 6 , y1 = 10 x2 = 3 , y2 = 8 & x = 4 , y = 6 Using section formula x = ( 1 2 + 2 1)/( 1 + 2) 4 = ( 3 +1 6)/( +1) 4 = (3 6)/( +1) 4(k + 1)= 3k 6 4k 4 = 3k 6 4k 3k = 6 + 4 7k = 2 k = ( 2)/( 7) k = 2/7 Hence, the ratio is k : 1 = 2/7 : 1 Multiplying 7 both sides = 7 2/7 : 7 1 = 2 : 7 So, the ratio is 2: 7