Unit 7: Class 9 Math PECTAA Notes New Book

Introduction

HSA Notes brings short, clear, exam focused notes designed to help Class 9 SSC Part One Matric students score 90 plus marks in Punjab Board exams under the New Book 2026 to 2027 session.

This page covers Unit 7, Coordinate Geometry, from Exercise 7.1, 7.2, 7.3 & Review Exercise 7 including identifying the location of points on the coordinate plane and calculating the distance between two points.

HSA Notes Features

• Short, easy to remember definitions.
• Step by step solutions for every question.
• Tricks and memory aids for faster revision.
• Exact alignment with the PCTB and PECTAA textbook.
• Point locations simplified into a clear, repeatable method.
• Past paper pattern questions included throughout.
• A fast revision format built for last minute review.
• Trusted by Punjab students.

Available Across All Punjab Boards and Top Schools

These notes are built for students across all Punjab Boards, including Lahore, Gujranwala, Rawalpindi, Faisalabad, Bahawalpur, Multan, Sargodha, Sahiwal, and DG Khan, and are used at top schools including The City School, Beaconhouse, Roots International, Lahore Grammar School, Karachi Grammar School, Froebel’s, The Educators, Army Public School, Divisional Public School, and Government Model School.

Exercise 7.1, Q1, Point Locations

Exercise 7.1, Q2, Distance Between Two Points

This part uses the distance formula, d equals the square root of the sum of the squared differences of the x-coordinates and the y-coordinates: d = √[(x₂ − x₁)² + (y₂ − y₁)²]. The full step by step calculations for every part of Q2 are included in the downloadable PDF.

How to Identify a Point’s Location

To work out where a point sits on the coordinate plane, check the sign and value of each coordinate one at a time rather than trying to visualise the whole plane at once. First look at the x-coordinate: if it is positive, the point sits somewhere to the right of the y-axis; if negative, to the left; if exactly zero, the point lies on the y-axis itself.

Next look at the y-coordinate the same way: positive means above the x-axis, negative means below, and zero means the point lies on the x-axis. Once both signs are known, combine them to name the quadrant. Positive x with positive y places the point in Quadrant I, negative x with positive y in Quadrant II, negative x with negative y in Quadrant III, and positive x with negative y in Quadrant IV.

Special cases follow the same logic: when both coordinates are zero the point is the origin, and when a condition names an exact value such as x = 3, the point lies on that fixed vertical or horizontal line rather than in an open region. Watch carefully for “greater than” versus “greater than or equal to,” since the first excludes the boundary line or axis and the second includes it, a distinction that shows up often in past paper questions.

How to Apply the Distance Formula

The distance formula grows directly out of the Pythagorean theorem: the horizontal gap between two points and the vertical gap between them form the two legs of a right triangle, and the straight-line distance between the points is the hypotenuse.

To use it, first label the two given points as (x₁, y₁) and (x₂, y₂). Subtract the x-coordinates to find the horizontal difference, and subtract the y-coordinates to find the vertical difference. Square both differences, since squaring removes any negative sign and keeps the two legs additive.

Add the two squared values together, then take the square root of that sum to arrive at the distance. It does not matter which point is labelled first and which is labelled second, since squaring a difference gives the same result whether the difference itself is positive or negative. Keeping the substitution organised, coordinate by coordinate, is the easiest way to avoid sign errors under exam time pressure.

Why This Unit Matters for Your Overall Score

Coordinate geometry begins with these two foundational skills, reading a point’s location directly from its coordinates and measuring the distance between two points, because both ideas recur throughout the rest of the unit and into later topics such as the midpoint formula, slope, and the equations of lines.

A firm grasp of quadrants and axes now makes every later diagram easier to read at a glance, while comfort with the distance formula prevents small arithmetic slips from compounding into larger errors in longer, multi-step problems.

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Frequently Asked Questions

How do I find which quadrant a point belongs to? Check the sign of the x-coordinate and the y-coordinate separately. Positive x and positive y give Quadrant I, negative x and positive y give Quadrant II, negative x and negative y give Quadrant III, and positive x and negative y give Quadrant IV.

What does it mean if a point has x = 0 or y = 0? If x equals 0, the point lies on the y-axis. If y equals 0, the point lies on the x-axis. If both equal 0, the point is the origin.

What is the formula for the distance between two points? d = √[(x₂ − x₁)² + (y₂ − y₁)²], found by subtracting the corresponding coordinates, squaring each difference, adding the results, and taking the square root.

Are these notes aligned with the PCTB and PECTAA textbook? Yes, these notes are built to exactly match the PCTB and PECTAA New Book for Class 9 Mathematics for the 2026 to 2027 session.

Conclusion

With Exercise 7.1 fully solved, covering point locations and the distance formula, Class 9 students have a strong foundation for Unit 7, Coordinate Geometry. Use these notes alongside regular practice with past papers to build the confidence needed for 90 plus marks in your Punjab Board exam.

Best of luck for your Class 9 Mathematics exam!