Coordinate Geometry | निर्देशांक ज्यामिति

Goal of this chapter: By the end of this lesson, you will feel confident with the key NDA-level concepts of Coordinate Geometry and be able to solve exam-style questions on your own.

हिंदी Note: इस chapter को आराम से पढ़िए – examples और छोटे-छोटे अभ्यास के साथ। एक बार समझ आ गया तो NDA में Coordinate Geometry के सवाल आपके लिए बहुत आसान हो जाएंगे 😄

Overview | परिचय

Coordinate Geometry is the study of geometric figures using coordinate systems. It helps in solving problems involving distances, areas, slopes, and equations of lines.
निर्देशांक ज्यामिति वह विषय है जिसमें हम ज्यामितीय आकृतियों को निर्देशांक पद्धति की सहायता से हल करते हैं।

Key Formulas & Tips | प्रमुख सूत्र व युक्तियाँ

1. Distance between two points: √[(x2 - x1)² + (y2 - y1)²]

2. Mid-point of a line: ((x1 + x2)/2 , (y1 + y2)/2)

3. Slope of a line: m = (y2 - y1)/(x2 - x1)

4. Equation of a line: y - y1 = m(x - x1)

5. Area of triangle with given vertices: ½|x1(y2−y3)+x2(y3−y1)+x3(y1−y2)|

Examples with Hints | उदाहरण और संकेत

Q1. Find the distance between A(2, 3) and B(5, 7).

Hint: Use the distance formula.

Q2. Find the mid-point of the line joining (4, 8) and (10, 2).

Hint: Use mid-point formula.

Q3. What is the slope of the line joining (1, 2) and (4, 6)?

Hint: Slope = (y2 - y1)/(x2 - x1)

Q4. Write the equation of line passing through (3, -2) with slope 2.

Hint: Use y - y1 = m(x - x1)

Q5. Find the area of triangle with vertices (1, 2), (4, 5), (7, 8).

Hint: Use area formula for triangle using coordinates.

Practice Questions | अभ्यास प्रश्न

Q1. Distance between (1,1) and (4,5)? → Answer: 5

Q2. Mid-point between (6, 3) and (2, 1)? → Answer: (4, 2)

Q3. Slope of line joining (5, 5) and (10, 10)? → Answer: 1

Q4. Equation of line through (0,0) with slope 3? → Answer: y = 3x

Q5. Area of triangle with vertices (0,0), (4,0), (0,3)? → Answer: 6

Ask Doubt

Quick Recap | सार

Now you should be able to:

Recall the key ideas of this chapter without looking at the book.
Solve most NDA-style questions of this topic step by step.
Identify and avoid the most common traps used in competitive exams.

Self-check: अगर practice questions अपने आप हो रहे हैं, तो chapter strong है। जो सवाल अटकते हैं, बस उन्हें दोबारा देख लें।

Common Exam Mistakes | आम गलतियाँ

जल्दी-जल्दी में question पूरा पढ़े बिना solve करना।
Sign (+/−) या power गलत लिख देना।
Last step में calculation check न करना – आधा काम सही, answer गलत।

ध्यान रखिए: NDA में topper वो नहीं जो सब कुछ जानता है, बल्कि वो है जो छोटी-छोटी गलतियाँ avoid कर देता है।