Straight Lines
Orthocentre
JEE Main 2023
Grade 11
Question:
If $(\alpha, \beta)$ is the orthocentre of the triangle $ABC$ with $A(3, -7), B(-1, 2), C(4, 5)$, find $9\alpha - 6\beta + 60$.
Step-by-Step Solution
Key Concept: Write the altitude from $A$ perpendicular to $BC$ and the altitude from $B$ perpendicular to $AC$. Solve simultaneously for $(\alpha, \beta)$, then evaluate the expression.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: 25