In the rectangular trapezoid oabc, CB ‖ OA, CB = 8, OC = 8, ∠ oaba = 45 ° (1) calculate the coordinates of points a, B and C; (2) calculate the area of △ ABC

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• 1. In trapezoidal ABCO, OC ∥ AB establishes a plane rectangular coordinate system with o as the origin. The coordinates of a, B and C are a (8,0), B (8,10) and C respectively In trapezoidal ABCO, OC ‖ The coordinates of a, B and C are a (8,0), B (8,10) and C (0,4) respectively. Point d (4,7) is the midpoint of line BC, and the moving point P starts from point O and moves along the route of broken line OAB at the speed of 1 unit per second. The moving time is T seconds (1) Find the analytical formula of the straight line BC; (2) Let the area of △ OPD be s, the functional relationship between S and t is obtained, and the value range of independent variable t is pointed out; (3) When t is, the area of △ OPD is the same as that of trapezoidal oabc
• 2. As shown in the figure, in the rectangular coordinate system, one side of an acute triangle AOB coincides with the positive half axis of the X axis, and the other side OA intersects the image of the function y = 1 / X at point P. take point P as the center of the circle, take 2PO length as the radius, draw an arc to intersect the image of y = 1 / X at point R, and make parallel lines of the X axis and Y axis through points P and R respectively to obtain the rectangular pqrm, connecting OM
• 3. As shown in the figure, the two right angle sides OA and ob of RT △ ABC are respectively on the positive half axis of X axis and the negative half axis of Y axis, and C is a point on OA As shown in the figure, the two right angle sides OA and ob of RT △ ABC are respectively on the positive half axis of X axis and the negative half axis of Y axis, C is a point on OA, OC = ob, and the parabola y = (X-2) (x-m) - (P-2) (P-M) (where m and P are constants, and M + 2 ≥ 2p > 0) passes through two points a and C (1) It is proved that: (P, 0) is on a parabola; (2) The length of OA and OC is represented by M and P respectively; (3) When m and P satisfy what relation, the area of △ AOB is the largest
• 4. As shown in the figure, it is known that there is a straight line and a curve in the rectangular coordinate system. The straight line and the positive half axis of 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 function y = 12x 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-axis and y-axis are m, n, Line AB intersects PM and PN at points E and f respectively (1) Calculate the coordinates of points E and f respectively (use the algebraic expression of a to represent the coordinates of point E, and use the algebraic expression of B to represent the coordinates of point F, only need to write the results, not the calculation process); (2) Calculate the area of △ OEF (the result is expressed by the algebraic formula containing a and b); (3) The values of AF and be are calculated respectively (the results are expressed by algebraic expressions containing a and b); (4) Please prove whether △ AOF and △ BOE are necessarily similar; if they are not necessarily similar or not, briefly explain the reasons. Solutions: (1) point E (a, 1-A), point F (1-B, b); (2 points) (2) S △ EOF = s rectangular monp-s △ emo-s △ fno-s △ EPF, =ab-12a(1-a)-12b(1-b)-12(a+b-1)2, =12 (a + B-1); (4 points) （3）BE=a2+(1-1+a)2=2a, AF = (1-1 + b) 2 + B2 = 2B; (6 points) (4) (7 points) It is proved that: OA = ob = 1, ∴∠FAO=∠EBO； ∵ point P (a, b) is a point on the curve y = 12x, 2 ab = 1, that is AF &; be = 1; OA and ob = 1, ∴AFOB=OABE； Why is 2Ab = 1, that is AF ﹥ 8226; be = 1; Why is 2Ab = 1?
• 5. The pointer starts from "12" and points to 1 after clockwise rotation of () degrees
• 6. The pointer rotates clockwise from 12 around point 0 () to "3" The pointer rotates clockwise from 12 around point 0 () to "3" The pointer rotates 180 ° clockwise from 3 around point 0 to () The pointer rotates 90 ° clockwise from 5 around point 0 to () A cuboid is 6cm long, 4cm wide and 5cm high. Its surface area is () square centimeter Its volume is () cubic centimeter The length, width and height of a cuboid are 8 decimeters, 3 decimeters and 5 decimeters respectively. The total length of its edges is () decimeters, and the formula is () A cuboid has a bottom area of 10 square meters, a height of 3.6 meters and a volume of () cubic meters The edge of a cube is 6 decimeters long, and its surface area is () square decimeters
• 7. Given that the line x = 2Y + 2, how can we know the linear equation that the line rotates 90 degrees (such as counterclockwise), if we can, rotate any angle
• 8. The abscissa of a point P on the line X-Y + 1 = 0 is 3. If the line rotates 90 ° counterclockwise around the point P to get a line L, then the equation of line L is______ ．
• 9. If the line y = x + 3-1 is rotated 15 ° counterclockwise around a point (1, 3) above it, the equation of the line is______ ．
• 10. The equation of a straight line with y = 2x + 1 rotated 90 degrees anticlockwise and passing through point (1,2)
• 11. In the rectangular trapezoid oabc, CB / / OA, CB = 10, OC = = 10, OAB = 45 °. Find the coordinates of a, B, C
• 12. As shown in the figure, in the right angle trapezoid oabc, CB ‖ OA, CB = 8, OC = 8, ∠ OAB = 45 ° (1) calculate the coordinates of points a, B and C; (2) calculate the area of △ ABC
• 13. As shown in the figure, in the right angle trapezoid oabc, AB / / OC, O are the origin of the coordinate graph, point a is on the positive half axis of Y axis, and point C is on the positive half axis of X axis
• 14. If the quadratic function y = (M + 1) x square + m square - 2m-3 passes through the origin, find M
• 15. Given that f (x) is a quadratic function, if y = (x) obtains the minimum value of - 4 at x = 2, and the image of y = f (x) passes through the origin, the function y is obtained
• 16. Given that the fixed-point coordinates of the square + K image of the quadratic function y = (x + m) are m (1, - 4), the focal coordinates of the function image and the x-axis are obtained
• 17. Given the quadratic function y = (x + m) square + K image The vertex coordinates are (3 / 2, - 1 / 4) Finding function relation The intersection coordinates of image and x-axis When x is what value, Y > 0, = 0, < 0?
• 18. When does the image of quadratic function pass through the origin?
• 19. The quadratic function y = x ^ - 4x + 5 is a curve about the symmetric movement of x-axis, Y-axis and origin
• 20. Quadratic function y = xsquare - 4x + 1, find the function analytic formula of the image about the Y axis, the image analytic formula of the X axis, and the image analytic formula of the origin centrosymmetry