Subjects geometry

Distance B Ac 9Dc5Af

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1. **Problem statement:** Calculate the shortest distance from point B to line AC. 2. **Formula and explanation:** The shortest distance from a point to a line is the perpendicular distance. If the coordinates of points A, B, and C are known, the distance $d$ from point B to line AC can be calculated using the formula: $$d = \frac{|(x_C - x_A)(y_A - y_B) - (x_A - x_B)(y_C - y_A)|}{\sqrt{(x_C - x_A)^2 + (y_C - y_A)^2}}$$ This formula comes from the area of the parallelogram formed by vectors and dividing by the base length. 3. **Intermediate work:** Substitute the coordinates of points A, B, and C into the formula. 4. **Explanation:** This formula calculates the absolute value of the cross product of vectors divided by the length of AC, giving the perpendicular distance. 5. **Final answer:** The shortest distance from B to AC is the value obtained from the formula above, in kilometers. (Note: Since the exact coordinates are not provided, the numeric answer cannot be computed here.)