Question: If the points (2K, K)(K, 2K) and (K, K) with $K > 0$enclose triangle of area 18 square u...

Question

If the points (2K, K)(K, 2K) and (K, K) with $K > 0$ enclose triangle of area 18 square units then the centroid of triangle is equal to

Answer 1

Solution

$\Delta = \frac{1}{2}\left| \begin{matrix} 2K & K & 1 \\ K & 2K & 1 \\ K & K & 1 \end{matrix} \right| = 18$ ⇒ $\frac{K^{2}}{2} = 18$ ⇒ $K = \pm 6$ . Consider K = +6 because K > 0, then the points (12, 6) (6,12) and (6,6).

Hence, centroid = $\left( \frac{12 + 6 + 6}{3},\frac{6 + 12 + 6}{3} \right) = (8,8)$

Question: If the points (2*K, K*)(*K*, 2*K*) and (*K*, *K*) with \(K > 0\)enclose triangle of area 18 square u...

Solution

Question: If the points (2K, K)(K, 2K) and (K, K) with \(K > 0\)enclose triangle of area 18 square u...