As shown in the figure, in rectangular ABCD, ab = 30, ad = 40, P is a moving point on BC, passing through point P as PM ⊥ AC at point m, PN ⊥ BD at point n, let's ask if point P is at BC Does the value of PM + PN change during movement? If it does not change, calculate the value; if it changes, try to point out the range of change

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• 1. As shown in the figure, in the isosceles triangle ABC, point P is a moving point on the bottom edge AC, and m and N are the midpoint of AB and BC respectively. If the minimum value of PM + PN is 2, then the perimeter of △ ABC is___ ．
• 2. The length of segment Mn is 2 cm, and point P is the golden section point of segment Mn
• 3. Given that the segment Mn = 4cm, point P is the golden section point, find the length of the longer segment MP
• 4. Given the line segment Mn = 4cm and the point P is the golden section point, find the length of the longer line segment MP?
• 5. P is the golden section point of segment Mn, MP is greater than Mn, and MP = (root 5-1), then what is Mn equal to?
• 6. If the distance between M and N on the plane is 17cm, P is another point on the plane, and PM + PN = 25cm, then ： 1. Point P is on line Mn 2. Point P must be on line Mn 3. Point P is outside the line Mn 4. Point P must
• 7. The distance between two points Mn on the plane is 17cm. If there is a point P on the plane and the sum of the distance between two points Mn is equal to 25cm, then the following conclusion is correct A. Point P is on the line Mn. B, P must be outside the line Mn. C, point P must be outside the line Mn. D, point P may be on the line Mn or outside the line Mn
• 8. As shown in the figure, make a point P, make PE = PF, and make the distance from point P to both sides of ∠ AOB equal
• 9. M. The distance between two points of n is 10cm, and there is a little p, which satisfies PM + PN = 13cm A. Point P must be on line Mn B. Point P must be outside the line Mn C. Point P may be on or outside the line Mn D. None of the above is true
• 10. Given: angle ABC and two points m, N. calculate: point P, so that PM = PN, and the distance from point P to both sides of ABC is equal
• 11. P is a moving point on the edge of rectangle ABCD, ab = 3, BC = 4, PM and PN are the distances to the diagonal respectively. Prove that (PM + PN) is a fixed value and calculate this value Did not learn the trigonometric function rectangle topic
• 12. As shown in the figure, the two diagonals of diamond ABCD are 6 and 8 long respectively. Point P is a moving point on diagonal AC, and points m and N are the midpoint of edge AB and BC respectively. Then the minimum value of PM + PN is______ ．
• 13. In the RT triangle ABC, ∠ ACB = 90 °, P is the point on AB, PM ⊥ AC at point m, PN ⊥ BC at point n and PM = PN, AC = 6, BC = 8, then PM =? Text description
• 14. It is known that in y1-y2, Y1 is positively proportional to 1 / x, the scale coefficient K1, Y2 is inversely proportional to 1 / x, the scale coefficient K1, Y2 is inversely proportional to 1 / x, and the scale coefficient K2, When x = 1, y = 4, then the relationship between K1 and K2 is ['<' > '='] , quick search /
• 15. How many intersections are there in the rectangular coordinate system of the same plane between the function y = K1 / X and the function y = K2 * x (K1, K2 > 0)
• 16. As shown in the figure, it is known that the image of the inverse scale function Y1 = K1 / X (K1 > 0) and the linear function y2 = k2x + 1 (K2 ≠ 0) intersect at two points a and B, and AC is perpendicular to the X axis and at point C If the area of triangle OAC is 1 and AC = 2oC The analytic expressions of inverse proportion function and linear function are obtained Given that point B is (- 2, a), please observe the image and point out why the value of X is, Y1 > Y2
• 17. It is known that Y1 is positively proportional to X (scale coefficient is K1), Y2 is inversely proportional to X (scale coefficient K2), If the image of function y = Y1 + Y2 passes through point (1,10) (2, - 1), then what is y = when x = 7?
• 18. Let y = Y1 + Y2, where Y1 is inversely proportional to x, and the scaling coefficient is K1, Y2 is positively proportional to X & sup2; and the scaling coefficient is K2= K 2 Given that y = y1-y2, Y1 is positively proportional to the square root of X, Y2 is inversely proportional to X & sup2; and y = 0 when x = 1; y = 31 / 4 when x = 4, the functional relationship between Y and X is obtained The first problem y = 0 to find the relationship between K1 and K2
• 19. It is known that y = Y1 + Y2, where Y1 is inversely proportional to 1 / x, and the scale coefficient is K1; Y2 is positively proportional to the square of X, and the scale coefficient is K2, x = - 1, y = 0, k1k2
• 20. As shown in the figure, in the plane rectangular coordinate system, the center of ⊙ P is (2, a) (a > 2), the radius is 2, and the length of the chord AB cut by ⊙ P is 23, then the value of a is () A. 22B. 2+2C. 23D. 2+3