Check sibling questions

Example 21 - Find distance of 4x - y = 0 from P (4, 1) - Examples

Example 21 - Chapter 10 Class 11 Straight Lines - Part 2
Example 21 - Chapter 10 Class 11 Straight Lines - Part 3
Example 21 - Chapter 10 Class 11 Straight Lines - Part 4
Example 21 - Chapter 10 Class 11 Straight Lines - Part 5
Example 21 - Chapter 10 Class 11 Straight Lines - Part 6

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Example 21 Find the distance of the line 4x – y = 0 from the point P (4, 1) measured along the line making an angle of 135° with the positive x-axis. There are two lines Line AB 4x – y = 0 Line CD making an angle 135° with positive x-axis Both lines meet at Q Point P(4, 1) is on line CD We need to find distance PQ. In PQ, P is (4,1) We need to find point Q Point Q is intersection of line AB & CD Equation of AB is 4x – y = 0 Finding equation of line CD Slope of line CD = tan 135° = tan (180° − 45°) = − tan 45° = − 1 Also, Point P(4, 1) lies on the line CD (4,1) & having slope –1 is In PQ, P is (4,1) We need to find point Q Point Q is intersection of line AB & CD Equation of AB is 4x – y = 0 Finding equation of line CD Slope of line CD = tan 135° = tan (180° − 45°) = − tan 45° = − 1 Also, Point P(4, 1) lies on the line CD (4,1) & having slope –1 is Equation of a line passing through a point (x1, y1)& having slope m is (y − y1) = m(x − x1) Equation of line CD passes through point P(4,1) & having slope –1 is (y − 1) = −1(x − 4) y − 1 = − x + 4 y + x = 4 + 1 x + y = 5 ∴ Equation of line CD is x + y = 5 Finding point Q Equation of AB : 4x − y = 0 Equation of CD : x + y = 5 Adding (1) & (2) 4x – y + x + y = 0 + 5 4x + x − y + y = 5 5x + 0 = 5 5x = 5 x = 5/5 = 1 Putting x = 1 in (1) 4x − y = 0 4(1) − y = 0 4 − y = 0 4 = y y = 4 Hence point Q (1, 4) Now we need to find distance between Q (1, 4) & P(4, 1) PQ = √((𝑥_2 − 𝑥_1 )^2+(𝑦_2 − 𝑦_1 )^2 ) = √((4−1)^2+(1−4)^2 ) = √(( 3)^2+(−3)^2 ) = √(9+9) = √18 = √(9×2) = √(3^2 × 2) = = √(3^2 ) × √2 = 3√𝟐 units Hence the required distance is 3√2 units

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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.