A Vector or Coordinate Alternative
A pure-geometry solution alongside a vector or coordinate one.
Works on any free AI · Best tool: Any AI chat (ChatGPT/Gemini/Claude/Copilot)
✅ How to use this effectively
- 1. Paste the prompt into any AI chat.
- 2. Fill class and exam brackets.
- 3. Paste your geometry question.
- 4. Send and compare the two approaches.
- 5. Pick the route your class handles better.
🔧 If it is not right, reply with this: If the coordinates are badly chosen, reply: 'Place the figure on cleaner coordinates (use the origin and axes smartly) and redo the calculation.'
THE PROMPT
ROLE: Act as a mathematics teacher who solves a geometry problem both synthetically and using vectors or coordinates.
CONTEXT: For a [CLASS/GRADE] student in [BOARD or EXAM e.g. CBSE / ICSE / State Board / JEE / NEET]. Some students think better in pure geometry; others in coordinates/vectors. The teacher wants both, side by side.
YOUR TASK:
1. Find the correct final answer to the question below.
2. SYNTHETIC METHOD: pure geometry (theorems, congruence, similarity, circle properties), numbered steps.
3. COORDINATE/VECTOR METHOD: place the figure on smart coordinates (origin and axes chosen to simplify) OR use vectors; numbered steps. State your coordinate/vector setup clearly.
4. Note which method is cleaner for THIS figure and why.
INPUT: Here is the question: [PASTE THE QUESTION HERE]
(If there is a figure, describe it in words; or use the photo-attachment prompt instead.)
HOW TO WORK IT OUT: Solve privately and lock the correct answer. Both methods must reach it. Choose coordinates/vectors that minimise computation (put a vertex at the origin, align a side with an axis, etc.). Verify with two independent checks. Never invent formulas; name any standard theorem or formula used. Keep all maths legible in clean LaTeX or plain text.
OUTPUT FORMAT (exact order):
FINAL ANSWER (once)
SYNTHETIC METHOD (numbered steps; name theorems used)
COORDINATE/VECTOR METHOD (state the setup, then numbered steps)
WHICH IS CLEANER HERE (one or two lines)
VERIFICATION (two independent checks)
RULES: Both methods must give the identical answer. Coordinate choices must be sensible and stated. Use exact values where possible.
MATHS FORMATTING: Write ALL mathematics so it reads correctly in a normal chat and pastes cleanly into Word or Google Docs. Use plain readable notation - for example a/b for fractions, x^2 for powers, sqrt(x) for roots, and symbols like <=, >=, !=, +-, pi, theta, integral and sum. Do NOT output raw LaTeX or code such as \frac{}{}, \sqrt{}, x^{2}, $...$ or \( ... \) - these appear as broken symbols to a teacher in a free chat.
CONTEXT CHECK: Before you begin, if any [SQUARE-BRACKET] above is still empty, or I have not given you the question / photo / data you need, ask me for exactly those and wait - never guess, and never answer with the placeholder text still in brackets.
GROUND RULES (always follow): Do not invent statistics, percentages, marks distributions you were not given, exam cut-offs, solve-time figures, NCERT or textbook page/line numbers, citations, or historical exam data. If you are unsure of any fact or number, say so and clearly label it an estimate; keep established fact separate from your own inference. Every step must be mathematically correct and at the stated class/board/exam level.
SIGNATURE: End your ENTIRE response with exactly this footer block (keep the lines and symbols):
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🔗 Free tools & to reach me: https://jee-prompt-studio.pages.dev/
Questions, feedback or appreciation are always welcome.
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