Prove that M lies in plane BDG and CM is perpendicular to it.

01 / Standard#Your turn

E=(0,0,0),\ C=(1,1,1),\ B=(1,0,1),\ D=(0,1,1),\ G=(1,1,0)

Official paper · jm02-2026 · 1(b) · PDF 3

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Find one linear equation satisfied by B,D,G.

Hint 2

Compare its normal with the direction of EC.

Worked solution

The three noncollinear vertices determine the plane.
$BDG:\ x+y+z=2,\quad\mathbf n=(1,1,1)$
M satisfies the plane equation and CM is parallel to its normal.
$\frac23+\frac23+\frac23=2,\quad\overrightarrow{CM}=-\frac13(1,1,1)$

M∈plane BDG and CM⊥plane BDG.

Checks and common pitfalls: Perpendicularity to one line alone does not establish perpendicularity to a plane.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
The three noncollinear vertices determine the plane.
$BDG:\ x+y+z=2,\quad\mathbf n=(1,1,1)$
M satisfies the plane equation and CM is parallel to its normal.
$\frac23+\frac23+\frac23=2,\quad\overrightarrow{CM}=-\frac13(1,1,1)$

Think first. Reveal a hint when the class is ready.

2026 JM02