Question:
The area of the triangle formed by the points \( (a,b+c), (b,c+a), (c,a+b) \) is
The area of the triangle formed by the points \( (a,b+c), (b,c+a), (c,a+b) \) is
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If determinant = 0 → points lie on same line.
Updated On: May 1, 2026
- \( abc \)
- \( a^2+b^2+c^2 \)
- \( ab+bc+ca \)
- \( 0 \)
- \( a(ab+bc+ca) \)
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The Correct Option is D
Solution and Explanation
Concept: Area = 0 if points are collinear.
Step 1: Use determinant formula.
Step 2: Form matrix: \[ \begin{vmatrix} a & b+c & 1 b & c+a & 1 c & a+b & 1 \end{vmatrix} \]
Step 3: Expand determinant.
Step 4: Simplify terms → all cancel.
Step 5: Area = 0 ⇒ collinear points.
Step 1: Use determinant formula.
Step 2: Form matrix: \[ \begin{vmatrix} a & b+c & 1 b & c+a & 1 c & a+b & 1 \end{vmatrix} \]
Step 3: Expand determinant.
Step 4: Simplify terms → all cancel.
Step 5: Area = 0 ⇒ collinear points.
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