(1) Please write the coordinates of point C directly;
(2) If point B is in the first quadrant, ∠OAB =∠ Oba, the symmetry point of point B about the origin O is point D. 。
① Try to judge the shape of quadrilateral ABCD and explain the reasons;
② The existing moving point P starts from point B and moves along the BA-AD route to the end point D at a speed of 1 unit per second, while another moving point Q starts from point A and moves along the AC direction to the end point C at a speed of 0.4 unit per second. When one of the moving points reaches the end point, the other moving point stops moving. It is known that AB=6, and the moving time of set points P and Q is t seconds. During the exercise,
Analysis of 28 Questions in Quanzhou, Fujian Province in 2009. (This little question is 13)
Solution: (1) c (-5,0) ........................ (3 points)
(2)① The quadrilateral ABCD is rectangular for the following reasons:
As shown in the figure, it is known that A, O and C are on the same straight line, and OA = OCb? , O, D are on the same straight line, and OB=OD, ∴ quadrilateral ABCD is a parallelogram ............................................ (5 points).
∵∠OAB=∠OBA∴OA=OB, that is, ac = 2oa = 2ob = bd.
∴ Quadrilateral ABCD is a rectangular ............................................................... (7 points).
② As shown in the figure, the quadrilateral ABCD starting from ① is a rectangle.
∴∠ CBA =∞∠ ADC = 90 .................... (8 points).
AB=CD=6，AC= 10。
∴ From Pythagoras theorem, BC=AD=
=? = 8 .........................(9 points)
∵? ,? , ∴ 0 ≤ t ≤14 .......................... (10 score)
When 0≤t≤6, point P is on AB and PQ is connected.
∫AP is the diameter, ∴∠ PQA = 90 ...................... (11min) [Source: Z, xx, k.Com]
And ∠PAQ=∠CAB, ∴△PAQ∽△CAB.
∴? , that is? T = 3.6 ...................... (12 points)
When 6 < t ≤ 14, point P is on AD and PQ is connected.
Similarly, ∠ PQA = 90, △PAQ∽△CAD.
∴? , that is? T-6，t= 12。
To sum up, when the moving point Q is on a circle with a diameter of PA, the value of t is 3.6 or 12...( 13 minutes).
2. (Lanzhou, Gansu, 2009) 29. (The full mark of this question is 9) As shown in Figure ①, square? In ABCD, the coordinates of point A and point B are (0, 10), (8, 4),?
Point c is in the first quadrant. Moving point p is in the square? On the edge of A → B → C → D, start from point a and move at a constant speed along a → b → c → d.
At the same time, the moving point Q moves on the positive semi-axis of the X axis at the same speed. When point P reaches point D, both points stop moving at the same time.
Let the movement time be t seconds. [Source: Subject Network ZXXK] [Source: Zxxk.Com]
(1) When point P moves on edge AB, what is the abscissa of point Q? The function image of (length unit) motion time t (second) is shown in Figure ②. Please write down the coordinates when point Q starts to move and the moving speed of point P;
(2) Find the coordinates of the side length and vertex c of the square;
(3) When the value of t is (1), the area of △OPQ is the largest, and the coordinates of point P at this time are found;
(4) If the original velocities of point P and point Q remain unchanged, can OP and PQ be equal when point P moves at a uniform speed along A→B→C→D? If yes, write all qualified values of t; If not, please explain why.
You can only insert one picture at a time, so I can only give you one question. . . Please forgive me.