NCERT Class 12 · Ch 4 Exercise 4.2 · Q5
NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.2 Question 5
The triangle with vertices (2,−6),(5,4),(k,4) has area 35 square units. Find k.
💡 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: D: k=12 or −2.
- The horizontal base between (5,4) and (k,4) has length |k−5|; its perpendicular height from (2,−6) is 10.
- Therefore ½×10×|k−5|=35, giving |k−5|=7.
- Thus k−5=7 or −7, so k=12 or −2. Both cases have area 35.
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