Let the area of the triangle with vertices A 1 , α , B α , 0 and C 0 , α be 4 sq. units. If the points α , - α , - α , α and α 2 , β are collinear, then β is equal to

Step-by-step solution

Given, the area of the triangle with vertices A 1 , α , B α , 0 and C 0 , α be 4 sq. units Now applying formula for area we get, 1 2 α 0 1 1 α 1 0 α 1 = ± 4 ⇒ α = ± 8 Now given points will be 8 , - 8 , - 8 , 8 , 64 , β OR - 8 , 8 , 8 , - 8 , 64 , β Given above points are collinear, so their slope will be equal, so slope= 8 + 8 - 8 - 8 = - 1 ⇒ β - 8 64 + 8 = - 1 ⇒ β = - 64