NCERT Class 12 · Ch 4 Exercise 4.2 · Q4
NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.2 Question 4
Using determinants, find the line through (i) (1,2),(3,6); (ii) (3,1),(9,3).
💡 Concept Hints
- Identify whether this needs determinant expansion, an inverse, or the absolute determinant formula for area.
- For a determinant use signed cofactors. For a system first check invertibility; for an area take half the absolute determinant.
✅ Step-by-Step Solution
Final Answer: (i) y=2x; (ii) y=x/3.
- A point (x,y) is on a line through two fixed points exactly when their 3×3 coordinate determinant is zero.
- (i) Expanding det [[x,y,1],[1,2,1],[3,6,1]]=0 gives −4x+2y=0, hence y=2x.
- (ii) Expanding det [[x,y,1],[3,1,1],[9,3,1]]=0 gives −2x+6y=0, hence y=x/3.
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