Bihar Board Class 10 · Maths · Matric exam 2027
Chapter 7: Coordinate Geometry — notes
The chapter’s 6 parts in the book’s order — the first idea of each and the points Medha Ma’am writes on the board — and the summary at the end. The full lesson and a check question for each part are in the app.
1. Locating a point: coordinates
Okay, so, to locate a point on a plane, we need a pair of coordinate axes.
- • x-coordinate (abscissa) = distance from y-axis
- • y-coordinate (ordinate) = distance from x-axis
- • Point on x-axis: (x, 0)
- • Point on y-axis: (0, y)
2. The Distance Formula
Okay, so imagine town B is 36 km east and 15 km north of town A.
- • Distance formula: PQ = √[(x2–x1)² + (y2–y1)²]
- • Distance from origin: OP = √(x² + y²)
- • Example: P(3,2), Q(–2,–3), R(2,3)
- • PQ = √50, QR = √52, PR = √2
- • PQ² + PR² = QR² → angle P = 90°
- • So PQR is a right triangle
3. Using the Distance Formula
Okay, so the distance formula can do more than just find lengths.
- • Square check: all 4 sides equal, both diagonals equal
- • Collinear check: AB + BC = AC means points lie in a line
- • Equidistant point: set AP² = BP², simplify
- • Example 4: relation found is x – y = 2
- • Example 5: point on y-axis equidistant from A(6,5), B(–4,3) is (0, 9)
4. The Section Formula
Okay, so — think of a telephone company placing a relay tower at P, between A and B.
- • Section formula (ratio m1 : m2):
- • x = (m1x2 + m2x1)/(m1+m2)
- • y = (m1y2 + m2y1)/(m1+m2)
- • Mid-point formula: ((x1+x2)/2, (y1+y2)/2)
- • Example 6: ratio 3:1 of (4,–3),(8,5) → point (7, 3)
- • Example 8: trisection points of A(2,–2),B(–7,4): (–1,0) and (–4,2)
5. Finding ratio, and the parallelogram idea
Okay, so sometimes we're given a point, and we need to find in what ratio it divides a segment.
- • To find ratio: use section formula, solve for m1:m2 or k:1
- • On y-axis, abscissa (x) = 0
- • On x-axis, ordinate (y) = 0
- • Diagonals of a parallelogram bisect each other
- • Example 10: mid-point AC = mid-point BD → p = 7
6. Area of a Triangle
Okay, so you already know area of a triangle = ½ × base × altitude, and you've used Heron's formula too.
- • Area = ½ |x1(y2–y3) + x2(y3–y1) + x3(y1–y2)|
- • Area is always taken as a positive (numerical) value
- • Area = 0 means the points are collinear
- • Example 11: vertices (1,–1),(–4,6),(–3,–5) → area 24 sq units
- • Example 12: vertices (5,2),(4,7),(7,–4) → area 2 sq units
- • Quadrilateral: split into 2 triangles, add their areas
Summary
Okay, so let's look back at everything in this chapter. We started with how to locate a point — using its abscissa and ordinate. A point on the x-axis looks like (x, 0), and a point on the y-axis looks like (0, y). Then we moved to the distance formula, PQ = √[(x2 − x1)² + (y2 − y1)²]. Remember, this came from the Pythagoras theorem. We used it to check if points form a triangle, a square, if they're collinear, or if a point is equidistant from two given points. After that came the section formula — it gives the coordinates of a point dividing a line segment in a ratio m1 : m2. The mid-point formula is just a special case of this, where the ratio is 1 : 1. We used these to find ratios, trisection points, and even to show that a parallelogram's diagonals bisect each other. Finally, we found the area of a triangle using Area = ½|x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2)|. Here's something neat — if this area comes out to 0, the three points are collinear. And we even used this to find the area of a quadrilateral, by splitting it into two triangles. So, tell me — out of all these, which formula did you enjoy using the most?
AskMedha · Medha Ma’am — Bihar Board Class 10 Maths, Chapter 7. Written from the textbook, checked twice.
Questions parents and students ask
- How do I get the "Coordinate Geometry" notes as a PDF?
- Press "Save as PDF" — the phone’s print sheet opens; choose "Save as PDF" there. The PDF holds the notes only.
- Where are these notes written from?
- From the chapter’s own textbook text, part by part, in the book’s own terms; a second, independent model then checked every part against the book. The full lesson, a check question for each part and the practice are in the AskMedha app.
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