To find the coordinates of the point that is three-tenths of the way from point \( A \) to point \( B \), we can use the formula for finding a point along the line segment connecting two points. The formula to determine the coordinates \( P(x, y) \) that divides the segment \( AB \) in the ratio \( m:n \) is given by:
\[ P = \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right) \]
In this case:
- Point \( A(-4, -5) \) (denoted as \( (x_1, y_1) \))
- Point \( B(12, 6) \) (denoted as \( (x_2, y_2) \))
- You want to find the point \( P \) that is \( \frac{3}{10} \) of the way from \( A \) to \( B \). This means it is \( 3 \) parts towards \( B \) and \( 7 \) parts towards \( A \). Thus, the ratio \( m:n = 3:7 \).
Now we can plug in the values into the formula:
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Calculate for the x-coordinate: \[ x = \frac{3(12) + 7(-4)}{3 + 7} = \frac{36 - 28}{10} = \frac{8}{10} = 0.8 \]
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Calculate for the y-coordinate: \[ y = \frac{3(6) + 7(-5)}{3 + 7} = \frac{18 - 35}{10} = \frac{-17}{10} = -1.7 \]
Combining the two results, the coordinates of the point three-tenths of the way from \( A \) to \( B \) are:
\[ \boxed{(0.8, -1.7)} \]