A(h,-6),B(2,3) and C(-6,k) are the coordinates of vertices
of a triangle whose centroid is G(1,5). Find h and k.

Explanation

To find the values of \( h \) and \( k \) for the triangle with vertices \( A(h, -6) \), \( B(2, 3) \), and \( C(-6, k) \) whose centroid is \( G(1, 5) \), we can use the formula for the centroid of a triangle. The centroid \( G \) of a triangle with vertices \( (x_1, y_1) \), \( (x_2, y_2) \), and \( (x_3, y_3) \) is given by:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) \]

### Step 1: Set up the equations for the x-coordinates

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