NCERT Mathematics, Class 10, textbook pages 99–112

How to help your child with Class 10 Maths Chapter 7, Coordinate Geometry, at home

Distance and section formulas, explained for parents: a 45-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

(x₁,y₁)(x₂,y₂)midpoint

NCERT Class 10 Maths Chapter 7 Coordinate Geometry: what it teaches

Your teen finds distances between points with the distance formula, divides a segment in a given ratio with the section formula, finds midpoints, and checks if points form particular shapes.

Why it matters later. Coordinate geometry continues with straight lines and conics in Class 11.

See it: this chapter in pictures

(−5, 7) to (−1, 3)√(4² + 4²)= 4√2
Brackets around negatives.
divide (4,−3)–(8,5) in 3 : 1((3·8 + 1·4)/4, (3·5 − 3)/4)= (7, 3)
Weighted average of coordinates.
midpoint of (2,3), (6,9)((2+6)/2, (3+9)/2)= (4, 6)
Average the coordinates.

You need

  • graph paper
  • a map with a grid

Tonight’s 45 minutes

  1. Find the distance between (−5, 7) and (−1, 3) (4√2).
  2. Find the midpoint of (2, 3) and (6, 9) (4, 6).
  3. Find the point dividing (4, −3) and (8, 5) in 3 : 1 (7, 3).
  4. Check whether (1, 5), (2, 3), (−2, −11) are collinear.

Words to use

  • distance formula
  • section formula
  • midpoint
  • collinear
  • ratio

Watch for

  • Sign slips with negative coordinates. Put brackets around every coordinate before subtracting.
  • Using ratio m : n in the wrong order. The point nearer the first point uses the smaller share.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

YouDistance (0,0) to (3,4)?

Your child√(9 + 16) = 5.

A game for this week: Map treasure

  1. Mark points on a grid map.
  2. Give distance and ratio clues.
  3. Find the treasure point.
  4. Swap roles.

A 5-day plan, 45 minutes a day

  1. Day 1Explain-back.
  2. Day 2Worked examples.
  3. Day 3Practice set.
  4. Day 4Real-life problem.
  5. Day 5Mixed quiz.

Everyday moments to practise

  • GPS and maps.
  • Game design.
  • Architecture layouts.
  • Sports field positions.

Quick check

Ask these at the end of the week. Tap to see the answer.

Distance between (0, 0) and (3, 4)?

5.

Midpoint of (2, 3) and (6, 9)?

(4, 6).

Point dividing (4, −3), (8, 5) in 3 : 1?

(7, 3).

Ready for the next chapter when your child…

  • Uses the distance formula.
  • Uses section and midpoint formulas.
  • Tests collinearity.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Mathematics (Class 10). See the full Class 10 parent guide for every chapter.

Questions parents ask

What is the distance formula?

√((x₂ − x₁)² + (y₂ − y₁)²).

What is the midpoint formula?

((x₁ + x₂)/2, (y₁ + y₂)/2).

Is area of triangle in the syllabus?

It may be deleted in the current syllabus; check your school.