**Ex 10.3, 10**

Last updated at March 9, 2017 by Teachoo

Last updated at March 9, 2017 by Teachoo

Transcript

Ex 10.3, 10 The line through the points (h, 3) and (4, 1) intersects the line 7x – 9y – 19 = 0. at right angle. Find the value of h. Let the equation of line AB be 7x – 9y – 19 = 0 Let point (h, 3) be C(h, 3) & point (4, 1) be D(4, 1) Let CD be the line passing through points C(h,3) & D(4,1) Given line CD intersects line AB at right angle So, line AB and CD are perpendicular We know that, product of slope of perpendicular lines is –1 So, (Slope of line AB) × (Slope of line CD) = –1 Finding slope of line AB – 9y = − 7y + 19 y = ( − 7𝑥 + 19)/( − 9) y = (( − 7)/( − 9))x + ((−19)/9) y = 7/9x + ((−19)/9) The above equation is of the form y = mx + c where m = slope of line So, Slope of line AB = 7/9 Now finding slope of line CD Line CD passes through points C(h, 3) and D(4, 1) Slope of a line passing through points (x1,y1) & (x2,y2) is = (𝑦_2 − 𝑦_1)/(𝑥_2 − 𝑥_1 ) So, Slope of line CD passing through points C(h, 3) and D(4, 1) = (1 − 3)/(4 − ℎ) = ( − 2)/(4 − ℎ) Thus, slope of line CD = ( − 2)/(4 − ℎ) From (1) (Slope of line AB) × (Slope of line CD) = –1 Putting values 7/9 × 2/(ℎ − 4) = − 1 14/(9(ℎ − 4)) = − 1 14 = − 9(h − 4) 14 = −9h − 9( − 4) 14 = −9h + 36 14 − 36 = − 9h − 22 = − 9h ( − 22)/( − 9) = h 22/9 = h h = 22/9 Thus, value of h is 22/9

Ex 10.1, 5
Important

Ex 10.1, 7 Important

Ex 10.1, 9 Important

Ex 10.1, 13 Important

Ex 10.2, 8 Important

Ex 10.2, 14 Important

Ex 10.2, 18 Important

Example 15 Important

Ex 10.3, 5 Important

Ex 10.3, 8 Important

Ex 10.3, 10 Important You are here

Ex 10.3, 16 Important

Ex 10.3, 18 Important

Example 22 Important

Misc 6 Important

Misc 12 Important

Misc 18 Important

Misc 23 Important

Important Question for exams Class 11

- Chapter 1 Class 11 Sets
- Chapter 2 Class 11 Relations and Functions
- Chapter 3 Class 11 Trigonometric Functions
- Chapter 4 Class 11 Mathematical Induction
- Chapter 5 Class 11 Complex Numbers
- Chapter 6 Class 11 Linear Inequalities
- Chapter 7 Class 11 Permutations and Combinations
- Chapter 8 Class 11 Binomial Theorem
- Chapter 9 Class 11 Sequences and Series
- Chapter 10 Class 11 Straight Lines
- Chapter 11 Class 11 Conic Sections
- Chapter 12 Class 11 Introduction to Three Dimensional Geometry
- Chapter 13 Class 11 Limits and Derivatives
- Chapter 14 Class 11 Mathematical Reasoning
- Chapter 15 Class 11 Statistics
- Chapter 16 Class 11 Probability

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.