The two vertices of triangle are (2,-1),(3,2) and the third vertex lies on x+y=5 . The area of the triangle is 4 units, then the third vertex is

Step-by-step solution

Since, the third vertex (x₁, y₁ ) lie on the line x+y=5 aligned x₁+y₁ &=5 y₁ &=5-x₁ aligned Coordinate of C is (x₁, 5-x₁ ) Given, area of A B C=4 units array lc 1 2 | array ccc 2 & -1 & 1 3 & 2 & 1 x₁ & 5-x₁ & 1 array |=4 Using R₂ R₂-R₁ and R₃ R₃-R₁, & | array ccc 2 & -1 & 1 1 & 3 & 0 x₁ & -2 & 6-x₁ & 0 array |=8 6-x₁-3 (x₁-2 )= 8 6-x₁-3 x₁+6= 8 12-8=4 x₁ or 4 x₁=20 x₁=1 or x₁=5 y₁=5-1=4 or y₁=0 array C (x₁, y₁ )=C(1,4) or C(5,0)