Example 17 - Chapter 10 Class 11 Straight Lines (Term 1)
Last updated at Dec. 8, 2016 by Teachoo
Last updated at Dec. 8, 2016 by Teachoo
Transcript
Example 17 Find the equation of a line perpendicular to the line x 2y + 3 = 0 and passing through the point (1, 2). Let equation of line AB be x 2y + 3 = 0 And let point P be P(1,-2) Let line CD be perpendicular to line AB & passing through point P(1,-2) Lets first calculate slope of line AB x 2y + 3 = 0 2y = x 3 2y = (x + 3) 2y = x + 3 y = ( + 3)/2 y = x/2 + 3/2 y = 1/2 x + 3/2 The above equation is of the form y = mx + c where m is the slope Thus, slope of line AB = 1/2 We know that product of slope of perpendicular lines is 1 Here, line AB is perpendicular to line CD Slope of line AB Slope of line CD = 1 1/2 Slope of line CD = 1 Slope of line CD = 1 2/1 Slope of line CD = 2 Thus, line CD has a slope 2 , passes through point P(1, 2) We know that, equation of line having slope m and passing through point (x1,y1) is y y1 = m(x x1) Putting values for line CD, x1 = 1, y1 = 2 & m = 2 y ( 2) = 2 (x 1) y + 2 = 2(x 1) y + 2 = 2x + 2 y + 2 + 2x 2 = 0 y + 2x = 0 y = 2x Thus, the required equation of line is y = 2x
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