Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KCET2018MathematicsDeterminants

If ( (x₁, y₁ ), (x₂, y₂ ) ) and ( (x₃, y₃ ) ) are the vertices of a triangle whose area is ' ( k ) ' square units, then [ | array ccc x₁ & y₁ & 4 x₂ & y₂ & 4 x₃ & y₃ & 4 array |² is ]

Options

  1. A( 32 k ² )
  2. B( 16 k ² )
  3. C( 64 k ² )
  4. D( 48 k ² )

Correct answer

C. ( 64 k ² )

Step-by-step solution

Vertices of a triangle are ( (x₁, y₁ ), (x₂, y₂ ) ) and ( (x₃, y₃ ) . ) So, area of triangle is given by, ( 1 2 | array lll x₁ & y₁ & 1 x₂ & y₂ & 1 x₃ & y₃ & 1 array |=k ) We have [ array l | array lll x₁ & y₁ & 4 x₂ & y₂ & 4 x₃ & y₃ & 4 array |²=16 | array lll x₁ & y₁ & 1 x₂ & y₂ & 1 x₃ & y₃ & 1 array |² =16 (4 k² )=64 k² array ]

Practice Determinants on Quantrex Academy →

More from Determinants

Let A = [a_ ij ] be a square matrix of order 3 3 , where the elements are defined as a_ ij = cases i - 2j & if i = j 0 & if i > j 1 & if i < j cases then the value of |A^t| is 2026Let A be a square matrix of order 3 3 . If |A| = -4 , then the value of | A⁻¹ -2 | is: 2026Given P = bmatrix 2 & & 1 1 & 2 & 2 1 & 3 & 3 bmatrix is the adjoint of a 3 3 matrix A and |A| = 3 , then the value of is: 2026Which of the following is correct? 2026If A and B are invertible square matrices of order n, then which of the following is not correct? 2026The system of equations x + 2y = 3 and 2x + 3y = 3 has 2026A value of lying between 0 and 2 and satisfying | array ccc 1+ ^2 & ^2 & 4 4 ^2 & 1+ ^2 & 4 4 ^2 & ^2 & 1+4 4 array |=0 2025If the inverse of [ array ccc -x & 14 x & 7 x 0 & 1 & 0 x & -4 x & -2 x array ] is [ array ccc 2 & 0 & 7 0 & 1 & 0 1 & -2 & 1 array ] , then | array ccc x & x+1 & x+2 x+1 & x+2 & x 2025 Full Determinants list All KCET PYQs