To find the coordinates of the point that is three-tenths of the way from point A to point B, we can follow these steps.
Given:
- Point A: \( A(-3, -8) \)
- Point B: \( B(10, 7) \)
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Find the difference in x-coordinates and y-coordinates: \[ \Delta x = x_B - x_A = 10 - (-3) = 10 + 3 = 13 \] \[ \Delta y = y_B - y_A = 7 - (-8) = 7 + 8 = 15 \]
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Calculate three-tenths of the way: \[ \text{Distance in x} = \frac{3}{10} \times \Delta x = \frac{3}{10} \times 13 = 3.9 \] \[ \text{Distance in y} = \frac{3}{10} \times \Delta y = \frac{3}{10} \times 15 = 4.5 \]
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Add these distances to the coordinates of point A: \[ x = x_A + \text{Distance in x} = -3 + 3.9 = 0.9 \] \[ y = y_A + \text{Distance in y} = -8 + 4.5 = -3.5 \]
Thus, the coordinates of the point that is three-tenths of the way from A to B are: \[ \boxed{(0.9, -3.5)} \]