Question:
A triangle has a vertex at \((1, 2)\) and the mid points of the two sides through it are \((-1, 1)\) and \((2, 3)\). Then the centroid of this triangle is :
A triangle has a vertex at \((1, 2)\) and the mid points of the two sides through it are \((-1, 1)\) and \((2, 3)\). Then the centroid of this triangle is :
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Use the midpoint formula to find the other two vertices, then average the three vertices.
Updated On: Nov 11, 2026
- \(\left(\frac{1}{3}, 2\right)\)
- \(\left(\frac{1}{3}, \frac{5}{3}\right)\)
- \(\left(1, \frac{7}{3}\right)\)
- \(\left(\frac{1}{3}, 1\right)\)
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The Correct Option is A
Solution and Explanation
Let \(A=(1,2)\). If \(B=(x_1,y_1)\) has midpoint \((-1,1)\) with A: \(\frac{1+x_1}{2}=-1\), \(\frac{2+y_1}{2}=1\), so \(B=(-3,0)\).
If \(C=(x_2,y_2)\) has midpoint \((2,3)\) with A: \(\frac{1+x_2}{2}=2\), \(\frac{2+y_2}{2}=3\), so \(C=(3,4)\).
Centroid \(=\left(\frac{1-3+3}{3}, \frac{2+0+4}{3}\right) = \left(\frac{1}{3}, 2\right)\).
Answer: (1) \(\left(\frac{1}{3}, 2\right)\)
If \(C=(x_2,y_2)\) has midpoint \((2,3)\) with A: \(\frac{1+x_2}{2}=2\), \(\frac{2+y_2}{2}=3\), so \(C=(3,4)\).
Centroid \(=\left(\frac{1-3+3}{3}, \frac{2+0+4}{3}\right) = \left(\frac{1}{3}, 2\right)\).
Answer: (1) \(\left(\frac{1}{3}, 2\right)\)
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