Question

\(\mathrm{A}(1,4), \mathrm{B}(4,1)\) and \(\mathrm{C}(x, 4)\) are the vertices of \(\triangle \mathrm{ABC}\). If the centroid of the triangle is \(\mathrm{G}(4, 3)\), then x is equal to ______.

पर्याय

• 2

• 1

• 7

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Answer 1

\(\mathrm{A}(1,4), \mathrm{B}(4,1)\) and \(\mathrm{C}(x, 4)\) are the vertices of \(\triangle \mathrm{ABC}\). If the centroid of the triangle is \(\mathrm{G}(4, 3)\), then x is equal to 7.

Explanation:

Using the centroid formula:

\(\frac{1 + 4 + x}{3} = 4\)

\(\Rightarrow 5 + x = 12\)

\(\Rightarrow x = 7\) 

Check y: \(\frac{4 + 1 + 4}{3} = 3\)