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As shown in the figure, the quadrilateral oabc is a right angled trapezoid. It is known that ab ∥ OC, BC ⊥ OC, the coordinates of point a are (3,4), ab = 6. (1) find out the analytic function of the straight line OA; (2) find out the perimeter of the trapezoid oabc; (3) if the moving point P moves along the direction of O ﹥ a ﹥ B ﹥ C (excluding O and C), and the distance of point P is s, write out the coordinates of point p; (expressed by the algebraic formula containing s) (4) if the straight line L passes through point d (3,0), and the line L divides the perimeter of right angle trapezoid oabc into two parts: 5:7
(1) Let the analytic expression of OA be y = KX, then the analytic expression of OA is y = 43x. (2) extend the Y-axis of Ba intersection at D. ∵ BA ∥ OC, ≁ ad ⊥ y-axis, and ad = 3, OD = 4, ∥ Ao = 5, ∥ DB = 3 + 6 = 9. ∥ OC = 9, BC = od = 4. ∥ coabc = OA + AB + BC + OC = 5 + 6 + 4 + 9 = 24. (3) when 0 & lt; s ≤ 5, P (35S, 45s); when 5 & lt; s ≤ 11, P (S-2, 4); when 11 & lt; S & lt; s ≤ 11, P; If the left part of L is 10, then s = 10-3 = 7, P (5,4). Let PD be y = MX + N, then 5m + n = 43M + n = 0 {M = 2n = - 6 ｜ y = 2x-6; if the left part of L is 14, then s = 14-3 = 11, ｜ P (9,4).. 9m + n = 43M + n = 0, then M = 23n = - 2 ｜ y = 23x-2
In the rectangular coordinate system xoy, we know that the image of function = 2x + B intersects with X axis and Y axis at points a and B respectively. If the area of triangle AOB is 4, then B=
f(x)=2x+b
When x is 0, f (x) = B, that is ob = B
When f (x) = 0, 2x + B = 0, x = - B / 2, that is OA length B / 2
Then B / 2 * B / 2 = 4
b=4
As shown in the figure, in the plane rectangular coordinate system, the images of two functions y = x, y = - 1 / 2S + 6 intersect at point a, the moving point P starts from point O and moves along the direction of OA at a speed of 1 unit per second, making the intersection line BC of PQ ‖ X axis at point Q, taking PQ as one side and making the body shape pqmn downward, let the area of its overlapping part with △ OAB be s
1 find the coordinates of point a
2 try to find out the relation between S and movement time t when point P moves on line OA
3 if point P continues to move in the original direction and speed after passing through point a, when the overlap area of square pqmn and △ OAB is the largest, the motion time t satisfies the condition that
FDDTRHTHY
As shown in the figure, in the rectangular coordinate system, the hyperbola y = K / X and the straight line y = 3 / 4x intersect at points a and B, and OA = 5 (1) find out the coordinates of two points a and B and the length of ob (2) in the second
As shown in the figure, in the rectangular coordinate system, the hyperbola y = K / X and the straight line y = 3 / 4x intersect at points a and B, and OA = 5
(1) Finding the coordinates of a and B and the length of ob
(2) Whether there is a point Q on the hyperbola of the first quadrant so that ∠ AQB = 90?; if there is, find the coordinate of point Q; if not, explain the reason
Hurry! Hurry!
If k > 0, and OA and ob are symmetrical, OB = 5
AB coordinates (2 √ 3K / 3, √ 3K / 2) (- 2 √ 3K / 3, √ 3K / 2) are obtained by solving the simultaneous equations
From OA = 5, k = 12, coordinates (4,3), (- 4, - 3)
The second question can be transformed into hyperbola y = K / X and circle x ^ 2 + y ^ 2 = 25, whether there are two different real roots in the first quadrant
Two equations are combined to get x ^ 4-25x ^ 2 + 144 = 0
The solution is x = 4 or x = 3
X = 4 is point a
So there is a q-point, and the coordinates are (3,4)
RELATED INFORMATIONS
- 1. As shown in the figure, it is known that there is a straight line and a curve in the rectangular coordinate system. This straight line, X axis and Y axis intersect at point a and point B respectively, and OA = ob = 1 This curve is a branch of the image of the function y = 2x / 1 in the first quadrant. Point P is any point on this curve, and its coordinates are (a, b). The perpendicular lines PM and PN made from point P to X and Y axes, and the perpendicular feet are m and n. the straight line AB intersects PM and PN at points E and f respectively. (1) it is proved that AF # 8226; be = 1 (2) the coordinates of points E and F are obtained respectively (the coordinates of point e are represented by the algebraic expression of a, and the coordinates of point e are expressed by the algebraic expression of A, Using the algebraic expression of B to express the coordinates of point F, we only need to write the results, not the calculation process); (3) Calculate the area of △ OEF (the result is expressed by the algebraic formula containing a and b); (4) Please prove whether △ AOF and △ BOE are necessarily similar; if not, briefly explain the reasons (5) When the point P moves on the curve y = 2x / 1, △ OEF changes accordingly. Point out the size of the angle whose size remains unchanged among the three internal angles of △ OEF, and prove your conclusion
- 2. Let the equation of the line L1 be x + 2y-2 = 0, and rotate the line L1 90 ° counterclockwise around the origin to get the line L2, then the equation of L2 is______ ．
- 3. The straight line M: x-2y = 0 rotates 45 degrees counterclockwise around the point P (2,1) to obtain the straight line L, and the equation of the straight line L is obtained
- 4. If the line X-Y + (3 ^ - 1) - 1 = 0 is rotated 15 degrees counterclockwise around points (1, 3 ^ - 1), the equation of the line L is?
- 5. In the plane Cartesian coordinate system, when the point a (4,2) is rotated 90 ° counterclockwise around the origin, the coordinate of the corresponding point a 'is____
- 6. Rotate the triangle 90 ° anticlockwise around point a for the first time, the second time and the third time respectively Rotate the triangle 90 ° anticlockwise around point a each time to draw the first, second and third rotation figures respectively. Use C1, C2 and C3 to represent the position of point C after rotation, and use number pairs to represent it. Connect C, C1, C2, C3 and C in turn to see what the figure is. Speed up
- 7. Draw a triangle AOB and rotate 90 ° counterclockwise around o point
- 8. Take a point p outside a right triangle ABC and rotate it 180 degrees counter clockwise. How to draw?
- 9. Draw the right triangle AOB rotated 180 degrees counterclockwise around point o
- 10. As shown in the figure, in the rectangular coordinate system, given the points a (- 3, 0), B (0, 4), make continuous rotation transformation for △ OAB, and get △ 1, △ 2, △ 3, △ 4 in turn , then the coordinates of the right angle vertex of △ 2014 are______ ．
- 11. The image of quadratic function y = 1 / 16 of the square is a parabola, and its focal coordinate is
- 12. As shown in the figure, in diamond shaped ABCO, the coordinates of point B are (3,3), and the coordinates of point C are () A. （0，2）B. （0，3）C. （0，2）D. （0，3）
- 13. The coordinates of points a, B and C are (3,0), (1, 3 under the root sign) and (0,1) respectively (4 / 4) the coordinates of points a, B and C are (3,0), (1, 3 under the root sign) and (0,1) respectively to find the area of the quadrilateral oabc
- 14. As shown in the figure, the vertices a, D and C of oabc and ADEF are on the coordinate axis, the point F is on the line AB, and the points B and E are on the function As shown in the figure, the vertices a, D and C of oabc and ADEF are on the coordinate axis, the point F is on the line AB, and the points B and E are on the function y = 1 / X (x)
- 15. If 1 + Tana / 1-taba = 3 + 2 √ 2, then sin2a How to simplify Cosa √ 2siina
- 16. Given x2 + y2 = 1, find the maximum and minimum of 2x + y Maximum value related to circle
- 17. Given that | X-Y + 1 | and X2 + 8x + 16 are opposite to each other, find the value of x2 + 2XY + Y2
- 18. Factorization factor: x2-2xy + y2-4=______ ．
- 19. [2/xy/(1/x+1/y)2+(x2+y2)/(x2+2xy+y2)]*2x/(x-y)
- 20. Given that C is the half focal length of the ellipse x2a2 + y2b2 = 1 (a > b > 0), then the value range of B + Ca is______ ．