(1) Find the side length BC;
(2) When t is what value, PC and BQ are equally divided;
(3) Connect PQ, let the area of △PBQ be y, explore the functional relationship between y and t, and find out what is the value of t and the maximum value of y? What is the maximum value?
As shown in the figure, AM∨BN, ∠ AE=x ∠ BC=y. 90, AB=4, point D is a moving point on the ray AM (point D does not coincide with point A), point E is a moving point on the line segment AB (point E does not coincide with points A and B), connecting de, and the intersection point E is the vertical line of de.
(1) When AD= 1, find the functional relationship between y and x, and write its definition domain;
(2) Under the condition of (1), take the midpoint f of the line segment DC and connect EF. If EF=2.5, find the length of AE;
(3) If the moving points D and E always meet the condition AD+DE=AB when moving, please explore: Does the perimeter of BCE change with the movement of points D and E? Please explain the reason.
As shown in the figure, in the rectangular coordinate system, the bottom AB of trapezoidal ABCD is on the X axis, and the endpoint D of the bottom CD is on the Y axis. The expression of straight line CB is y = -4/3x+ 16/3, and the coordinates of point A and point D are (-4,0) and (0,4) respectively. The moving point P starts from point A and runs on AB at a constant speed. The speed is 1 unit per second. When one of the moving points reaches the end point, they stop moving at the same time. When the point p moves t (seconds), the area of △OPQ is S (except for the moving point that cannot form △OPQ).
(1) Find the coordinates of point B and point C;
(2) Find out the functional relationship between S and T;
(3) When the value of t is what, what is the maximum value of s? And find the maximum value.
As shown in the figure, in the right-angled trapezoidal ABCD, AD∨BC, ∠ A = 90, AB= 12, BC=2 1, and AD = 16. The moving point P starts from point B and moves in the direction of ray BC at a speed of 2 units per second, and moves point Q..
(1) Let the area of △DPQ be s, and find the functional relationship between s and t;
(2) When t is what value, is the quadrilateral PCDQ a parallelogram?
(3) When t is what value, ①PD=PQ, ② DQ = PQ.
As shown in the figure, the side length of the square ABCD is 8cm, the moving point P starts from point A and moves from point A to point B at a constant speed of 1cm/ sec (point P does not coincide with points A and B), and the moving point Q starts from point B and moves along the dotted line BC-CD at a constant speed of 2cm/ sec. Point P and point Q start at the same time, and when point P stops, point Q also stops. Connect AQ.
(1) When point Q moves on BC line, how long after point P leaves, ∠BEP=∠BEQ?
(2) Let the area of △APE be ycm2 and AP=xcm, find the resolution function of Y about X, and write the definition domain of the function.
(3) When 4 < x < 8, find the range of function value y 。
As shown in the figure, in the rectangle ABCD, AB=3 and BC=4, the moving point P starts from point D and moves along DA to endpoint A, while the moving point Q starts from point A and moves along diagonal AC to endpoint C. When the intersection point P is PE∨DC and AC intersects with point E, the moving speed of moving points P and Q is 1 unit length per second and the moving time is x seconds.
(1) Find the functional relationship between y and x;
(2) Inquiry: When x is what value, is the quadrilateral PQBE a trapezoid?
(3) Are there such points P and Q, and the triangle whose vertices are P, Q and E is an isosceles triangle? If it exists, request all values of x that meet the requirements; If it does not exist, please explain why.
As shown in the figure, Rt△ABC, ∠ A = 90, AB= 10, AC=5. If the moving point P starts from point B and moves to point A along the BA line, the moving amount is 2 unit lengths per second. If the intersection point P is PM∨BC and the intersection point AC is at point M, let the moving time of the moving point P be x seconds and the length be AM.
(1) Find the functional relationship between Y and X, and write the range of the independent variable X;
(2) When x is what value, the area s of △BPM has the maximum value. What is the maximum value?
The side length of a square ABCD is 8 cm. The moving point P starts from point A and moves from point A to point B along the side AB at a constant speed of 1cm/sec (point P does not coincide with points A and B). The moving point q starts from the point b and moves at a constant speed of 2cm/sec along the dotted line BC-CD. Point p and point q start at the same time. When point P stops moving, point Q also stops moving. Connect AQ and pay BD.
(1) When point Q moves on BC line, after how long point P leaves, ∠BEP and ∠BEQ are equal;
(2) When the Q point moves on the BC line, it is proved that the area of △BQE is twice that of △APE;
(3) Let the area of △APE be y, try to find the resolution function of y about x, and write the definition domain of the function.
I hope it helps you.