LEARN · EXPLAIN · REVISE

Find the distance from P to the plane.

Read the idea, work independently, then explain what changed.

TOPIC 01

Introduction to solid geometry: mixed assessment

A mixed assessment: identify the method, justify it and revise your reasoning.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Standard#Your turn

P=(8,2,11),\quad\alpha:z=0

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Use perpendicularity tests with intersecting directions, then identify the relevant projection or section.

Hint 2

Drop a perpendicular parallel to the z-axis.

Worked solution

Use perpendicularity tests with intersecting directions, then identify the relevant projection or section.
Calculate or simplify this relation.
$H=(8,2,0),\quad PH=11$
Distance to a plane is the perpendicular length, not distance to the origin.

The requested value is 11.

Checks and common pitfalls: Distance to a plane is the perpendicular length, not distance to the origin.

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

Teacher preparation and assessment