Kenneth ChengMathematical modeling
← Senior Mathematics Studio

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Find the distance from P to the line.

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

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TOPIC 01

Equations of lines and circles: mixed review

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

What you will be able to explain

  • Connect the chapter skills without relying on the order of the exercises.

Try it. Leave your reasoning visible.

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

01 / Foundation#Your turn

Find the distance from P to the line.

P=(0,0),3x+4y−110=0P=(0,0),\quad 3x+4y-110=0
  • The denominator is the norm of the normal vector; parallel-line formulas require matched coefficients.
Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1
Translate the geometric condition into a coordinate equation.
Hint 2
Use this intermediate relation.
d=∣C∣/5d=|C|/5
Worked solution

  1. Translate the geometric condition into a coordinate equation.

  2. Apply the stated relation and retain its conditions.

    d=110/9+16=22d=110/\sqrt{9+16}=22

  3. The normal (3,4) has length 5.

The requested value is 22.

Checks and common pitfalls: The normal (3,4) has length 5.

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

Focus on one question

Teacher preparation and assessment

Question sequence

  • Ask students to name the relevant condition before calculating.

Board plan

  • Compare valid methods and annotate their conditions.

Anticipated thinking

  • A correct final value may still hide a missing assumption.

Assessment checklist

  • Check the method, conditions, reasoning and interpretation separately.

No sign-in. Work stays in this browser. Export before clearing browser data. Written reasoning is assessed with a checklist.

Curriculum and source notes ↗