Question

Find the value of k if (4, 4) is the centroid of the triangle with coordinates (2, 3), (k, 6) and (6, 3).

• A. 8
• B. 6
• C. 4
• D. 2

Answer 1

Answer:

C. 4

The correct answer is Option C (4).

The Centroid Formula

The centroid ($G$) of a triangle is the average of its vertices' coordinates. For three points $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$, the $x$-coordinate of the centroid is:
$x_{\text{centroid}} = \frac{x_1 + x_2 + x_3}{3}$

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1. Identify the $x$-coordinates:

   • Vertex 1: 2

   • Vertex 2: $k$

   • Vertex 3: 6

   • Centroid $x$: 4

2. Set up the equation:
   $4 = \frac{2 + k + 6}{3}$

3. Solve for $k$:

   • Multiply both sides by 3:
     $12 = 2 + k + 6$

   • Simplify the right side:
     $12 = 8 + k$

   • Subtract 8 from both sides:
     $k = 4$