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Prepositions after adjectives

Perpendicular: the correct preposition

Perpendicular is normally followed by to. With and at are not standard complements after this adjective.

Quick answer

Use perpendicular to

The standard construction is perpendicular to when describing lines, surfaces, directions, or angles. Perpendicular with and perpendicular at are generally nonstandard as direct combinations.

The wall is perpendicular to the floor.
Draw a line perpendicular to the axis.

Choose the pattern by meaning

These forms are not interchangeable. Choose the construction by meaning, not by which preposition appears most often.

1
perpendicular to + line or surface

Describing a right angle relationship

Use perpendicular to for geometry, direction, engineering, and physical position.

The beam is perpendicular to the support wall.
The path runs perpendicular to the river.
2
perpendicular to + movement or direction

Showing crossing directions

The phrase also describes motion or orientation at a right angle.

The aircraft moved perpendicular to the coastline.
The road lies perpendicular to the railway.

See the difference in context

The same subject can take different constructions because each sentence answers a different question.

Construction
Example
Meaning
perpendicular to
The two streets are perpendicular to each other.
Standard and widely used for right-angle relationships.
perpendicular with
The wall is perpendicular with the floor.
Nonstandard in current English; use perpendicular to.
perpendicular at
The line is perpendicular at the base.
At may describe a location separately, but not as the normal complement after perpendicular.

Common mistakes

Some combinations appear in real text but do not mean what learners often assume.

Using with instead of to

Perpendicular normally takes to.

✕ The pipe is perpendicular with the ceiling. ✓ The pipe is perpendicular to the ceiling.

Using at as the complement

At can describe position, not the geometric relationship itself.

✕ The road is perpendicular at the bridge. ✓ The road is perpendicular to the bridge.

Omitting the preposition

Perpendicular usually needs to before the second object.

✕ The lines are perpendicular each other. ✓ The lines are perpendicular to each other.

Quick practice

Choose the expression that matches the intended meaning.

1. The ladder is perpendicular ___ the ground.
2. The two lines are perpendicular ___ each other.
3. Which sentence is standard English?

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Frequently asked questions

Is perpendicular with ever correct?

It is generally considered nonstandard in modern English.

Can perpendicular describe movement?

Yes. You can describe movement or direction as perpendicular to something else.

Do mathematicians always use perpendicular to?

Yes. It is the standard mathematical and general English form.

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