**Example 18**

Last updated at March 11, 2017 by Teachoo

Last updated at March 11, 2017 by Teachoo

Transcript

Example 18 Find the equation of the line joining A(1, 3) and B(0, 0) using determinants and find k if D(k, 0) is a point such that area of triangle ABD is 3 sq units. Equation of line Let L be the line joining the A(1, 3) & B(0, 0) Let (x, y) be the third point on line Since all the there point lie on the same line, they do not from a triangle Hence, Area of triangle = 0 Thus, ∆ = 0 We know that Area of triangle is given by ∆ = 12 x1y11x2y21x3y31 Here, ∆ = 0 x1 = x , y1 = y x2 = 1 , y2 = 3 x3 = 0 , y3 = 0 Putting values 0 = 12 𝑥𝑦1131001 0 = 12 x 3101−y 1101+1 1300 0 = 12 ( x (3 – 0) – y (1 – 0) +1 (0 – 0)) 0 = 12 (x (3) – y (1) + 0) 0 = 12 (3x – y) 2 × 0 = 3x – y 0 = 3x – y 3x – y = 0 y = 3x Thus, the equation of line joining A & B is y = 3x Also given a point D (k, 0) & Area of triangle ∆ ABD is 3 square unit Since, Area of triangle is always positive , ∆ can have both positive and negative sings ∴ ∆ = ± 3 We have A : x1 = 1, y1 = 3 B : x2 = 0, y2 = 0 B : x3 = k , y3 = 0 Area of triangle is ∆ = 12 x1y11x2y21x3y31 ± 3 = 12 131001k01 ± 3 = 12 1 0101−3 01k1+1 00k0 ± 3 = 12 ( 1 (0 – 0) – 3 (k – 0) +1 (0 – 0)) ±3 = 12 (0 – 3 (k) + 0) ±3 = 12 ( –3k) ± 6 = – 3k So, 6 = – 3k or – 6 = – 3k

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Important Question for exams Class 12

- Chapter 1 Class 12 Relation and Functions
- Chapter 2 Class 12 Inverse Trigonometric Functions
- Chapter 3 Class 12 Matrices
- Chapter 4 Class 12 Determinants
- Chapter 5 Class 12 Continuity and Differentiability
- Chapter 6 Class 12 Application of Derivatives
- Chapter 7 Class 12 Integrals
- Chapter 8 Class 12 Application of Integrals
- Chapter 9 Class 12 Differential Equations
- Chapter 10 Class 12 Vector Algebra
- Chapter 11 Class 12 Three Dimensional Geometry
- Chapter 12 Class 12 Linear Programming
- Chapter 13 Class 12 Probability

About the Author

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.