Question:
If the points \( (2a,a), (a,2a), (a,a) \) form a triangle of area 18, find centroid
If the points \( (2a,a), (a,2a), (a,a) \) form a triangle of area 18, find centroid
Show Hint
Centroid is average of coordinates.
Updated On: May 1, 2026
- \( (4,4) \)
- \( (8,8) \)
- \( (-4,-4) \)
- \( (4\sqrt2,4\sqrt2) \)
- \( (6,6) \)
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The Correct Option is A
Solution and Explanation
Step 1: Use area formula (determinant).
Step 2: Compute determinant → area = \( a^2 \).
Step 3: Given area: \[ a^2 = 18 \Rightarrow a=3\sqrt2 \]
Step 4: Centroid formula: \[ \left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}\right) \]
Step 5: Substitute: \[ (4,4) \]
Step 2: Compute determinant → area = \( a^2 \).
Step 3: Given area: \[ a^2 = 18 \Rightarrow a=3\sqrt2 \]
Step 4: Centroid formula: \[ \left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}\right) \]
Step 5: Substitute: \[ (4,4) \]
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