3D Geometry
Image of Vertex in Plane — αβ+βγ+γα
nta_pyq_2023_apr
Grade 12
Question:
Two vertices of $\triangle ABC$: $(2,4,6)$, $(0,-2,-5)$; centroid $(2,1,-1)$. Third vertex $C=(4,1,2)$. Image of $C$ in $x+2y+4z=11$ is $(\alpha,\beta,\gamma)$. $\alpha\beta+\beta\gamma+\gamma\alpha$ is equal to
Step-by-Step Solution
Key Concept: Third vertex $C=3G-A-B=(4,1,2)$. Reflect $C$ in plane to find $(\alpha,\beta,\gamma)$.
$74$.
Correct Answer: 3