There are two villages a and B on the same side of the expressway. The vertical distances from them to the straight line Mn where the expressway is located are Aa1 = 2km, BB1 = 4km and A1B1 = 8km respectively. An exit P should be set between A1B1 of the expressway to minimize the sum of the distances between a and B villages and P. what is the shortest distance?

There are two villages a and B on the same side of the expressway. The vertical distances from them to the straight line Mn where the expressway is located are Aa1 = 2km, BB1 = 4km and A1B1 = 8km respectively. An exit P should be set between A1B1 of the expressway to minimize the sum of the distances between a and B villages and P. what is the shortest distance?

As shown in the figure: make a symmetrical point a 'of point a with respect to line A1B1, then connect a' B, intersect line A1B1 at point P, then AP + Pb is the minimum, and make BD ⊥ A1A extension line at point B at point D, ∵ Aa1 = 2km, BB1 = 4km, A1B1 = 8km, ∧ AA ′ = 4km, then a'd = 6km. In RT △ a 'dB, a' B = 62 + 82 = 10 (km), then AP + Pb is the minimum of 10km

Junior two mathematics questions for detailed answers
&If x is equal to half of √ 5 + √ 3, y = half of √ 5 - √ 3, find X of y plus y of X

Given the image intersection of hyperbola xy = - 8 and linear function y = 2 - X and two points a and B, the coordinates of two points a and B are obtained
There is a point P (m, n), M + n = 3 on the image of inverse scale function y = K / X (K ≠ 0), and P is on the image of y = - 4x. The analytic expression of inverse scale function is obtained
Given that ab < 0, point P (a, b) is on the image with inverse scale function y = B / x, then the line y = ax + B does not pass through the quadrant?

1. Substituting y = 2-x into xy = - 8, we get 2x-x * x = - 8, the solution is x = 4, x = - 2, and the coordinates are (4, - 2) (- 2,4)
2. M + n = 3, n = - 4m, M = - 1, n = 4, 4 = K / - 1, k = - 4
3. B = B / A, that is, B = Ab0, so it is only the second quadrant