Point P (- 3,1) the coordinates of the point obtained by rotating point P 90 ° around the origin are? (in two cases, clockwise and counterclockwise)

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• 1. The coordinates of point Q obtained by rotating point P (2,0) 90 ° counterclockwise around the origin o are____ 1. Point P (- 5,1-t) and point Q (k, 4) are symmetric with respect to the origin Then the value of 3k-2t is () A.-25 B.25 C.5 D.-5
• 2. Given that the coordinates of point P are (1,1), if point P is rotated 15 ° counterclockwise around the origin o of coordinates to get point Q, then the coordinates of point q are (,)
• 3. A (- 1,0) B (- 1,1), then the coordinates of a and B of the triangle ABO after rotating 45 degrees clockwise A and B coordinates when rotating 135 degrees clockwise
• 4. The ABC coordinate of triangle is known as a (- 6,4) B (- 3,6) C (- 1,2). Rotate the triangle 90 ° clockwise around point C 1. Find the coordinates of a and B after rotation 2. Calculate the area of the rotated figure ABCA
• 5. How to draw a triangle by turning it 90 ° anticlockwise around its outer point?
• 6. How to rotate a triangle 90 ° anticlockwise around point o?
• 7. Draw any △ ABC and make the following rotation: (1) with a as the center, rotate the triangle 40 ° counterclockwise (2) Take B as the center, rotate the triangle clockwise by 60 ° (3) take a point outside the triangle as the center, rotate the triangle clockwise by 120 ° (4) take the midpoint of AC as the center, rotate the triangle 180 ° to get the picture! Hurry
• 8. If a triangle is rotated 90 ° counterclockwise around a vertex, will each corresponding line segment in the original graph and the rotated graph be perpendicular to each other? Is there such a theorem?
• 9. As shown in the figure, rotate the right triangle abd 90 counterclockwise around the right vertex a to the position of the triangle ACF. The triangle abd is equal to the triangle ACF. The extension of BD intersects CF with point E and connects BC. If the angle FBE = angle CBE, try to determine the relationship between CE and BD (including the position relationship and quantity relationship),
• 10. Rotate the triangle ABO 90 degrees counterclockwise around point B
• 11. The equation of a straight line with y = 2x + 1 rotated 90 degrees anticlockwise and passing through point (1,2)
• 12. If the line y = x + 3-1 is rotated 15 ° counterclockwise around a point (1, 3) above it, the equation of the line is______ ．
• 13. 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______ ．
• 14. 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
• 15. 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
• 16. The pointer starts from "12" and points to 1 after clockwise rotation of () degrees
• 17. 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?
• 18. 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
• 19. 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
• 20. 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