Given the points a (1,1) and B (- 3,2), connecting the Y-axis of AB to the point P, then PA + Pb is the shortest. May I ask: is there a point m on the x-axis, so that Ma + MB is the shortest? If so, find out the coordinates of point m; if not, please explain the reason What are the coordinates of M

In the first case, let a be symmetric about X-axis a '(1, - 1), connect a'B, intersect X-axis at M (x, 0), let B (- 3,2), a' (1, - 1), let y = KX + Z, bring in B, a 'and solve y = - 3 / 4-1 / 4, thus m (- 1 / 3,0)
In the second case, point B 'is used, and the solution is the same as above

RELATED INFORMATIONS

1. Given that the image of the first-order function y = KX + B passes through the point (- 2,5) and intersects with the y-axis at the point P, the line y = - 12x + 3 intersects with the y-axis at the point Q, and the point q is exactly symmetric with the point P about the x-axis, the expression of the first-order function is obtained
2. Given that the image of the first-order function y = KX + B passes through the point (- 2,5) and intersects with the y-axis at the point P, the line y = - 12x + 3 intersects with the y-axis at the point Q, and the point q is exactly symmetric with the point P about the x-axis, the expression of the first-order function is obtained
3. Given that the image of a function y = KX + B passes through points m (- 1,1) and (0,2), let the image intersect with the x-axis at point a and with the y-axis at point B: Q: on the x-axis Given that the image of a function y = KX + B passes through point m (- 1,1) and point (0,2), let the image intersect with X axis at point a and Y axis at point B: Q: is there a point P on X axis, so that the triangle ZBP is an isosceles triangle? If it exists, the coordinates of all the points P that meet the conditions can be obtained. If not, please give reasons
4. It is known that the image of a function of degree passes through point a [2,3] and the ordinate of the intersection point with the y-axis is 4 Be detailed as soon as possible
5. It is known that the image of a linear function y = - 0.5x is parallel, and the intersection point (0, - 3) of the function and the Y axis is obtained
6. We know the quadratic function y = x ^ 2-mx-4. (1) prove that the image of the function must have two different intersections with the X axis; (2) let the coordinates of the intersection of the image of the function and the X axis be (x1,0), (x2,0), and 1 / X1 + 1 / x2 = - 1, find the value of M, and find the vertex coordinates of the function image. (please answer with junior high school mathematics knowledge)
7. The value of M is calculated on the x-axis through the intersection point of the image of the first-order function y = 3x + m and the image of the first-order function y = 4-2x
8. It is known that the image of a first-order function is parallel to the line y = 2x, and it intersects with the line y = - 3x-5 / 2 and has the same point on the y-axis
9. The graph of the function y = KX + B is parallel to the straight line y = 2x and passes through the point (0,3)
10. The graph of the function y = KX + B is parallel to the straight line y = 2x and passes through the point (0,3)
11. The rectangular white paper with the length of 38cm and the width of 5cm is glued together according to the method shown in the figure, and the glued part of the white paper is 2cm. (1) calculate the length of 10 pieces of white paper after gluing; (2) set the total length of X pieces of white paper after gluing as YCM, and write the functional relationship between Y and X
12. Mathematical problems of first degree function in the second grade of junior high school 1. A worker works from 7:00 to 11:00 in the morning. At first, he takes 15 minutes to prepare, and then processes a part every 15 minutes ① Find the functional relationship between Y in the morning time and X parts processed ② How many parts did he finish machining at 8 o'clock?
13. If Y-1 is proportional to 2-x, then the following statement is correct () A. Y is a linear function of X B. Y is a linear function of X C. It's a function of X, but it's not a positive scale function D. Y is not a function of X Is y a linear function of X? Why? y=-kx+2k+1 So if y is a function of X, is it a linear function? B is a positive proportional function
14. A mathematical problem of quadratic function in junior high school (speed) China is one of the countries with serious water shortage in the world. In order to enhance the residents' awareness of water saving, a municipal water supply company charges for the residents' water consumption by taking the household as the unit. That is to say, users with water consumption less than 10 tons (including 10 tons) per month will be charged a yuan per ton; users with water consumption more than 10 tons per month will still be charged a yuan per ton, and users with water consumption more than 10 tons will be charged a yuan per ton, The charge is B yuan per ton (b > A). If a household uses X tons of water per month, it should charge y yuan. The functional relationship between Y and X is shown in the figure 1. For the value of a, how much should a household charge for using 8 tons of water last month? 2. Find the value of B, and write the functional relationship between x > 10, y and X It is known that resident a used 4 tons more water last month than resident B. the two families charged 45 yuan. How many tons of water did they use last month?
15. A swimming pool has one intake gate and one discharge gate. A pool can be filled with water after 4 hours of water intake, and a pool can be finished after 6 hours of water discharge. When the water in the pool accounts for one fourth of the full pool, the intake gate and the discharge gate are opened at the same time. The opening time of the two gates is expressed by XH, and the percentage of the water in the pool is expressed by y (1) Find the functional relationship between Y and X, and write out the value range of the independent variable x; (2) Ask for the opening time of the two gates when the pool has one quarter of the water to one half of the water I feel like I'm going to be an idiot I can't do my homework
16. Given that the image of inverse scale function y = K / X (K ≠ o) intersects with the image of primary function y = KX + m (K ≠ 0) at a (2,1), find B
17. Ask a math question. About the inverse proportion function of grade three It is known that the intersection point in the first quadrant of the image of the first-order function y = x + m and the inverse scale function y = x / M + 1 (m ≠ 1) is p (XO, 3) (1) Finding the value of XO (2) Find the analytic expressions of the first-order function and the inverse proportion function
18. Two mathematics problems about inverse proportion function in grade three of junior high school 1. Point P is any point of the function y = 4 / X in the image of the first quadrant. The symmetrical point of point P about the origin is p ', passing through point P as PA parallel to the Y axis, passing through point P' as p'a parallel to the X axis, PA and p'a intersect at point A. when point P moves on the image, what will happen to the area of triangle app '? Explain the reason 2. It is known that the image of inverse scale function y = 1 / X and primary function y = 2x-1 has an intersection point a (1, a). Is there a point P on the x-axis, so that the triangle POA is an isosceles triangle? If so, explore the coordinates of point p; if not, explain the reason
19. If the image of the inverse scale function passes through points (1, 3) (1) find the analytic expression of the inverse scale function; (2) find the intersection coordinates of the primary function y = 2x + 1 and the image of the inverse scale function
20. It is known that the system of equations (x + 1) ^ 2 + y ^ 2 = 2, y = - x + B has a real solution, and the image of the inverse scale function y = 1 + B / X in each quadrant, y increases with the increase of X. if the point (a, 3) is on the hyperbola, find the value of A