The area of the triangle whose vertices are (-2, a)(2,-6) and (5,4) is 35 sq units then the value of ' a ' is

Step-by-step solution

The area of a triangle with vertices (x₁, y₁) , (x₂, y₂) , and (x₃, y₃) is given by the formula: Area = 1 2 |x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)| Substituting the given vertices (-2, a) , (2, -6) , and (5, 4) and the area 35: 35 = 1 2 |-2(-6 - 4) + 2(4 - a) + 5(a - (-6))| 70 = |-2(-10) + 8 - 2a + 5a + 30| 70 = |20 + 8 + 30 + 3a| 70 = |58 + 3a| This leads to two possible cases: Case 1: 58 + 3a = 70 3a = 12 a = 4 Case 2: 58 + 3a = -70 3a = -128 a = - 128 3 Comparing the results with the given options, a = 4 is pr