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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
Let L: y = k'x + B ∵ the included angle between M and l be 45 ° Tan 45 ° = | (k '- K) / (1 + k'k) |, that is: ± 1 = (k' - 1 / 2) / (1 + K '/ 2) it is concluded that: K' = 3 or K '= - 1 / 3 ∵ the line L is obtained from m by 45 ° counterclockwise ∵ K' > k, ∵ K '= 3 and ∵ the line L passes through point P (2,1)
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______ ．
The slope of the line L is - 1 because it passes through points (3, 4) and is perpendicular to the line X-Y + 1 = 0. The equation of the line L is y-4 = - 1 (x-3), that is, x + Y-7 = 0, so the answer is x + Y-7 = 0
The abscissa of a point P on the line 2x + y = 0 is 3. If the line rotates 90 degrees counterclockwise around the point P to get a line L, then the equation of the line ll is
Coordinates of point P: P (3, - 6)
If the line is rotated 90 degrees counterclockwise around point P, then the line L is the normal of the line
The slope of line l k = - 1 / (- 2) = 1 / 2
Let the line l be y = 1 / 2x + B and pass through the point P (3, - 6)
Then: y = 1 / 2x - 15 / 2
RELATED INFORMATIONS
- 1. 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?
- 2. 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____
- 3. 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
- 4. Draw a triangle AOB and rotate 90 ° counterclockwise around o point
- 5. Take a point p outside a right triangle ABC and rotate it 180 degrees counter clockwise. How to draw?
- 6. Draw the right triangle AOB rotated 180 degrees counterclockwise around point o
- 7. 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______ ．
- 8. In the plane rectangular coordinate system, the coordinates of vertex a of RT △ OAB are (3,1). If △ OAB is rotated 60 ° counterclockwise around point O, and point B reaches point B ', then the coordinates of point B' are______ ．
- 9. As shown in the figure, there are several points inside the square ABCD. These points and the vertices a, B, C and D of the square ABCD divide the original square into some triangles (not repeating each other) Can the original square be divided into 2008 triangles? How many points are inside the square ABCD One point is divided into four triangles, two points into six squares, and N points into (2n + 2) triangles
- 10. The side length of square ABCD is √ 2. If the intersection o of AC and BD is taken as the origin and OC is on the positive half axis of X axis, the coordinates of each vertex of square ABCD are
- 11. 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______ ．
- 12. 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
- 13. 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
- 14. The image of quadratic function y = 1 / 16 of the square is a parabola, and its focal coordinate is
- 15. 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）
- 16. 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
- 17. 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)
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- 19. Given x2 + y2 = 1, find the maximum and minimum of 2x + y Maximum value related to circle
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