1. Find out the route and speed of the moving point, so as to find out the length of the corresponding line segment;

2. Analyze several special positions of the motion midpoint to determine the range of independent variables;

1. The straight line and the coordinate axis intersect at two points respectively, and the moving point starts from the point and reaches the point at the same time, moving.

Stop. The point moves along the line at a speed of/kloc-0 per unit length per second, and the point moves along the line →→→→→

(1) Write the coordinates of two points directly;

(2) If the movement time of this point is seconds, the area of this point is a function of summation;

2. As shown in Figure 9, in a square AOCD with a side length of 1, m is the midpoint of AD, point P moves in the order of O-C-D-M, the distance traveled by point P is X, and the area of △OPM is Y. 。

(1) Find the functional relationship between y and x.

(2) Explore the coordinates of y= time point P.

(3) Is there no straight line passing through point (0,-1) to divide the area of square AOCD equally? If it exists, find the analytical formula of this straight line; If it does not exist, explain why.

3. In the plane rectangular coordinate system, point O is the coordinate origin, and the image of linear function y=-x+3 intersects with X axis and Y axis at points A and B respectively.

Intersect with the straight line y= x at point C.

(1) Find the coordinates of point C:

(2) The intersection point C takes the CD⊥x axis as the point D, and the point P starts from the point O and moves along the line segment OD to the end point D at the speed of 1 unit per second.

The vertical line with the crossing point P as the X axis intersects with the straight lines AB and OC at two points E and F respectively, and the movement time of the point P is t seconds, △ECF.

The area is s (s > 0), find the functional relationship between s and t, and directly write the range of independent variables;

(3) Under the condition of (2), is there a point Q on the Y axis that makes △EFQ an isosceles right triangle with EQ on the right?

If yes, find the qualified t value; If it does not exist, please explain why.

4. In rectangular coordinate system, right-angled trapezoid AODC, OA = 6, AB = BC, OB = 2, M is the midpoint of AC, and the abscissa is 4.

(1) Find the analytical formula of straight line AC;

(2) If point P and point Q start from point O and point D respectively, point P moves along the ray om at a speed of 2 unit lengths per second, and point Q moves at a speed of 2 unit lengths per second.

Move along the line segment DO at a speed of one unit length to the end point o, one point stops moving, and the other point stops moving. It is assumed that when moving,

Where t is, find the functional relationship between the area of △BPQ and t:

(3) Under the condition of (2), is there such a value of t that △PBC is a right triangle? If there is a value of t; If it doesn't exist

Yes, please explain why.

5. In the plane rectangular coordinate system, A (0 0,6), B (-2,0) and C (6 6,0) are folded along AC to get△ △ADC.

(1) Find the analytical formula of straight line AD;

(2) The moving point P starts from point B and moves to the end point C at the speed of 1 unit/second. When it passes through point P, it will be a straight line PM⊥x axis, and the two intersect.

AD, the straight line AB is in M and N, let the area of △BMN be S, and the movement time of point P be T seconds, and find the functional relationship between S and T, and

Find the range of t 。

7. As shown in the figure, in the isosceles right triangle ABC, O is the midpoint of hypotenuse AC, P is the moving point on hypotenuse AC, D is the point on BC, PB=PD, DE⊥AC, and the vertical foot is E. Verification: (1) PE = Bo;

(2) Let AC=2, AP=x, and the area of quadrilateral PBDE be y, find the functional relationship between Y and X, and write the definition domain of the function.