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

This depends on the point as the center to rotate a certain angle. After knowing this point, calculate the slope after rotation, and write the linear equation in the oblique form

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1. 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______ ．
2. If the line y = x + 3-1 is rotated 15 ° counterclockwise around a point (1, 3) above it, the equation of the line is______ ．
3. The equation of a straight line with y = 2x + 1 rotated 90 degrees anticlockwise and passing through point (1,2)
4. 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)
5. 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
6. 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 (,)
7. 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
8. 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
9. How to draw a triangle by turning it 90 ° anticlockwise around its outer point?
10. How to rotate a triangle 90 ° anticlockwise around point o?
11. 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
12. The pointer starts from "12" and points to 1 after clockwise rotation of () degrees
13. 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?
14. 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
15. 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
16. 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
17. 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
18. In the rectangular trapezoid oabc, CB / / OA, CB = 10, OC = = 10, OAB = 45 °. Find the coordinates of a, B, C
19. 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
20. 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