In what ratio does the point `(-4,\ 6)`divide the line segment joining the points `A(-6, 10)\ a n d\ B(3, -8)`?

Explanation

To find the ratio in which the point \((-4, 6)\) divides the line segment joining the points \(A(-6, 10)\) and \(B(3, -8)\), we can use the section formula. The section formula states that if a point \(P(x, y)\) divides the line segment joining two points \(A(x_1, y_1)\) and \(B(x_2, y_2)\) in the ratio \(m:n\), then the coordinates of point \(P\) can be expressed as:

\[ P\left(x, y\right) = \left(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\right) \]

### Step 1: Assign coordinates and ratio
Let the ratio in which point \(P(-4, 6)\) divides the line segment \(AB\) be \(k:1\). Thus, we can set \(m = k\) and \(n = 1\).
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