(1) When △EFG moves, find the time when point E moves to CD and AB respectively;
(2) After setting x (seconds), the overlapping area of △EFG and square ABCD is y(cm), and the functional relationship between y and x is found;
(3) Draw an approximate image of the function in (2) when 0≤x≤2 in the following rectangular coordinate system; If the circle centered on O intersects with the image at point P (x,) and the X axis intersects at point A and point B (A is on the left side of B), find the number of times ∠PAB.
2. As shown in the figure, in the right-angled trapezoid COAB CB‖OA, a plane rectangular coordinate system is established with O as the origin, and the coordinates of A, B and C are A (10/0,0), B (4 4,8), C (0 0,8), D is the midpoint of OA, and the moving point P starts from point A and moves along it.
(1) When the moving point P moves from A to B, let the area of △APD be S, try to write the functional relationship between S and T, point out the range of independent variables, and find the maximum value of S.
(2) Starting from the moving point P, a few seconds later, the line segment PD divides the area of the trapezoidal COAB into two parts: 1: 3? Find the coordinates of point p at this time.
3. As shown in the figure, in the plane rectangular coordinate system, the quadrilateral OABC is rectangular, and the coordinates of point A and point B are (3,0) and (3,4) respectively. Moving points M and N start from O and B at the same time, respectively, and move at the speed of 1 unit per second. Among them, point M moves to endpoint A along OA, and point N moves to endpoint C along BC ... Through point N as NP⊥AC, it crosses AC to P and connects MP. It is known that the moving point has moved for x seconds.
The coordinate of point (1)P is (,); (represented by an algebraic expression containing x)
(2) Find the maximum value of ⊿MPA area and the value of X at this time.
(3) Please explore: When X is what value, ⊿MPA is an isosceles triangle? How many situations have you found? Write your research results.
4. As shown in the figure, in the middle, 0,0 cm, the particle P moves at a uniform speed along a straight line from point A, and the particle Q moves at a uniform speed along a straight line from point D, the midpoint of AC, and gradually approaches the particle P. Let the velocities of the two particles P and Q be 1 cm/s and cm/s () respectively, and meet at a certain point E on the BC side one second later. (1) Find the length of AC and BC; (2) Will the point E where two particles meet be the midpoint of BC? Why? (3) If the triangle with vertices d, e and c is similar to △ABC, try to sum the values respectively;
5. In the triangle ABC, the existing moving point P starts from point A and moves in the direction of point B along ray AB; Moving point q starts from point c and moves in the direction of point b along ray CB. If the speed of point P is/sec and the speed of point Q is/sec, they start at the same time. Found: (1) After a few seconds, is the area of Δ δPBQ half that of ABC? (2) On the premise of (1), what is the distance between P and Q?
6. As shown in the figure, in the known right-angled trapezoidal ABCD, AD‖BC, ∠A=90o, ∠C=60o, AD=3cm, BC = 9cm. ⊙ O 1 Start from point A and follow the A-D-C polyline.
(1) Find the value of t when ⊙O2 is tangent to waist CD;
(2) In 0s
7. As shown in the figure, it is known that the lengths of trapezoidal AOBC(O is the origin), AC‖OB, OC⊥BC, AC and OB are the two roots of equation x2-(k+2) x+5 = 0 in rectangular coordinate system, and S △ AOC: S △ BOC = 1:.
(1) Fill in the blanks: 0c = _ _ _ _ _ _ _ and k = _ _ _ _ _ _ _
(2) Find another intersection of parabola through O, C and B. Moving points P and Q start from O and D at the same time, and both move at the speed of 1 unit per second, where point P moves from O to B along o B, point Q moves from D to C along DC, and the intersection point Q makes QM⊥CD pass through BC at point M, connecting △PMB and B.