Coordinate Geometry: JEE Main 2022 Mathematics question

Let the area of the triangle with vertices A(1, $\alpha$), B($\alpha$, 0) and C(0, $\alpha$) be 4 sq. units. If the points ($\alpha$, $-$$\alpha$), ($-$$\alpha$, $\alpha$) and ($\alpha$², $\beta$) are collinear, then $\beta$ is equal to :