Math topic中文

Cartesian coordinates

Cartesian coordinates in two dimensions

Practice questions

  1. 1直角坐标系中，点P(x,y)P(x,y)，xy<0xy < 0，x<yx < y，且PP到xx轴、yy轴的距离分别为33，77，则PP点的坐标为 ___ ．
  2. 2Sketch the graph in the spaces below. y=4xy = \frac{4}{x} y=−2x3y = -2x^{3} Hence, state the number of solutions for the equat…
  3. 3若点P（b-3，-2b）在y轴上，则点P关于x轴对称的点的坐标为（ ） A. （-3，0） B. （3，0） C. （0，-6） D. （0，6）
  4. 4Solutions to this question by accurate drawing will not be accepted. The diagram below shows a triangle ABC, with A(3,6)A(3,6)…
  5. 5在平面直角坐标系中，点A(−2,1)A(-2,1)，B(2,3)B(2,3)，C(a,b)C(a,b)，若BC/ ⁣/xBC/\!/x轴，AC/ ⁣/yAC/\!/y轴，则点CC的坐标为()(\quad) A. (−2,1)(-2,1) B. (2,−3)(2,-3)…
  6. 6The variables x and y are connected by the equation y=2x3−21x2+54xy = 2x^3 - 21x^2 + 54x. Some corresponding values of x and y are g…
  7. 7点A(sin⁡20180,tan⁡1170)A\left(\sin {2018}^{0},\tan {117}^{0}\right) 在直角坐标平面上位于第 象限．
  8. 8点M(2,−3)M(2,-3)到xx轴的距离是()() A. 22 B. −3-3 C. 33 D. 以上都不对
  9. 9已知线段MN/ ⁣/xMN/\!/x轴，点MM的坐标是(−3,5)(-3,5)，线段MNMN的长为66，则点NN的坐标是___.
  10. 10下列四个命题：①①带根号的数是无理数；②②如果∠A=∠B∠A=∠B，那么∠A∠A与∠B∠B是对顶角；③③经过直线外一点有且只有一条直线与已知直线平行；④④在平面直角坐标系中，如果点P(m,n)P(m,n)到xx…
  11. 11Complete the table of values for y=x−4x2y = x - \frac{4}{x^2}. Values are given to one decimal place where appropriate. Compl…
  12. 12已知点A（2，5）与点B（x，y）在同一条垂直于x轴的直线上，且B点到x轴的距离为3，那么点B的坐标是 ．
  13. 13The diagram shows a circle C1C_1 with centre P(5,3)P(5, 3). The circle touches the x-axis, the tangent OQ and another line Q…
  14. 14In the diagram, A(1, 2), B(8, 5), C(13, 7) and D(13, 2) are four points. Show that AB+BC=13.0AB + BC = 13.0, correct to 3 signif…
  15. 15The variables x and y are connected by the equation y=x+5x2−3y = x + \frac{5}{x^2} - 3 Some corresponding values of x and y are…
  16. 16The variables x and y are connected by the equation y=x35−2x+1y = \frac{x^3}{5} - 2x + 1. Some corresponding values of x and y a…
  17. 17已知抛物线y=ax2y=ax^{2}经过点A(2,1).(1)A(2,1).(1)求此抛物线的表达式;(2);(2)写出抛物线上点AA关于yy轴的对称点BB的坐标;(3);(3)求△OAB\triangle OAB的面积;(4);(4)…
  18. 18若点P(a+2,3−a)P(a+2,3-a)在第二象限，则(a−3)33−a2+4a+4=\sqrt[3]{(a-3)^{3}}-\sqrt{a^{2}+4a+4}=___.
  19. 19点M(−1,2)M(-1,2)在第___象限．
  20. 20Sketch the graph of y=−(x−2)2+4y=-(x-2)^2+4 on the axes below. Indicate clearly the coordinates of the points where the graph cro…
  21. 21点PP在第四象限，PP到xx轴的距离为66，PP到yy轴的距离为55，则点PP的坐标为 ___ ．
  22. 22如果xy>0,那么P(x,y)在第( )象限 A. 一 B. 二 C. 一、三 D. 二、 四
  23. 23The table shows some values for y=310x3−x+1y = \frac{3}{10}x^3 - x + 1 for −3≤x≤3-3 \le x \le 3. | x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |…
  24. 24在平面图上，点A(6,4)A(6,4)和点B(6,9)B(6,9)在同一列 ___ ((判断对错).).
  25. 25Complete the table of values for y=2x+20x−15y = 2x + \dfrac{20}{x} - 15. | x | 1 | 2.5 | 5 | 10 | 12.5 | 15 | 20 | |---|---|---|-…
  26. 26已知P（-3，-4），则P点到x轴的距离为（ ） A. 3 B. 4 C. 5 D. 3.5
  27. 27一次函数y=2x-6的图象与x轴的交点坐标是 ．
  28. 28The variables x and y are connected by the equation y=x35−2x+2y=\frac{x^3}{5}-2x+2. Some corresponding values of x and y are giv…
  29. 29In the diagram, the points P, Q and R have coordinates (9, -3), (6,1) and (18, -3) respectively. Find the length of PQ.…
  30. 30下列各点中，在过点(−2,2)(-2 , 2)和(−2,4)(-2 , 4)的直线上的是(    )(\:\:\:\:) A. (−2,0)(-2 , 0) B. (−3,−3)(-3 , -3) C. (3,2)(3 , 2) D. (5,4)(5 , 4)
  31. 31已知点P(2a−6,a+1)P(2a-6,a+1)，若点PP在坐标轴上，则点PP的坐标为___.
  32. 32ABCD is a parallelogram. A is the point (−6,−2)(-6,-2) and B is the point (−4,−7)(-4,-7). BC→=(8−2)\overrightarrow{BC} = \begin{pmatrix}8\\-2\end{pmatrix}…
  33. 33y=x34−2x+3y = \dfrac{x^3}{4} - 2x + 3. Complete the table of values for y=x34−2x+3y = \dfrac{x^3}{4} - 2x + 3. On the grid opposite, dra…
  34. 34点P在第四象限，若该点到x轴的距离是2，到y轴的距离是1，则点P的坐标是（ ） A. （-1，2） B. （-2，1） C. （2，-1） D. （1，-2）
  35. 35The diagram shows the speed-time graph of a motorcyclist. The shaded area represents the distance travelled. The distanc…
  36. 36已知平面直角坐标系中，点P（1-a，2a-5）到两坐标轴的距离相等，求a值并确定点P的坐标．
  37. 37从学校向东走600m，再向南走500m到达小伟家；从学校向南走500m，再向西走300m到小亮家，则小亮家在小伟家的 ．
  38. 38The table below is for the function y=x34−2x+1y = \dfrac{x^{3}}{4} - 2x + 1. Complete the table of values for y=x34−2x+1y = \dfrac{x^{3}}{4} - 2x + 1…
  39. 39下列说法正确的是()(\quad) A. y=kx+by=kx+b一定是一次函数 B. 有的实数在数轴上找不到对应的点 C. 长为3\sqrt{3}，4\sqrt{4}，5\sqrt{5}的三条线段能组成直角三角形 D.…
  40. 40A is the point (2,3) and B is the point (3,-5). Find the equation of the line AB. Answer ... Find the length of AB. Answ…
  41. 41The equation of the line l1l_1 is x+4y=20x + 4y = 20. The line cuts the x-axis at point A and the y-axis at point B. Another…
  42. 42当x= 时，点P（x-3，2）在y轴上．
  43. 43已知P(x,y)P(x,y)在第四象限，则Q(−x−3,−y+2)Q(-x-3,-y+2)在()(\quad) A. 第一象限 B. 第二象限 C. 第三象限 D. 第四象限
  44. 44点(−2，3)\left ( { -2，3 } \right )到y轴的距离为（ ） A. 3 B. −3-3 C. 2 D. −2-2
  45. 45点A（2，3）到x轴的距离为 ；点B（-4，0）到y轴的距离为 ；点C到x轴的距离为1，到y轴的距离为3，且在第三象限，则C点坐标是 ．
  46. 46The number of bacteria in a colony doubles every hour. The colony starts with: 50 bacteria. The table below shows the nu…
  47. 47The diagram below shows the sketch of the graph y = -x^2 + p x + q. The graph cuts the x-axis at points A and B(3, 0). T…
  48. 48Complete the table of values for y=2x2−2x.Valuesaregiventoonedecimalplacewhereappropriate.Onthegridopposite,drawthegraphofy=\dfrac{2}{x^{2}}-2x. Values are given to one decimal place where appropriate. On the grid opposite, draw the graph of …
  49. 49如果点P（2，b）在第四象限，则b的取值范围是___．
  50. 50Answer the whole of this question on a piece of graph paper. The variables x and y are related by the equation y=x3−3x2+1y = x^3 - 3x^2 + 1…
  51. 51The table of values for y=x+5x−7y = x + \dfrac{5}{x} - 7 is given below. | x | 0.5 | 1 | 1.5 | 2 | 3 | 4 | 5 | 6 | 7 | |---|--…
  52. 52已知点P的坐标为（2-a，3a+6），且点P到两坐标轴的距离相等，则a= ．
  53. 53P is the point (-3, 1) and Q is the point (3, 3). Find the length of the PQ. The point R is such that PQR forms an isosc…
  54. 54在平面直角坐标系中，点A（-2，4），B（3，4），连接AB，若点C为直线AB上的任何一点． （1）点C的纵坐标有什么特点？ （2）如果一些点在平行于y轴的直线上，那么这些点的横坐标有什么特点？
  55. 55在平面直角坐标系中，点(3,−5)(3,-5)到xx轴的距离为 ___.
  56. 56已知点AA到xx轴的距离等于22，则点AA的坐标是 ___ .(.(写出一个即可))
  57. 57如果点A(−5,−9)A(-5,-9)，则AA到xx轴的距离是()(\quad) A. −5-5 B. −9-9 C. 55 D. 99
  58. 58抛物线y=(x−1)2+2y=(x-1)^{2}+2与yy轴交点坐标为()() A. (0,1)(0,1) B. (0,2)(0,2) C. (1,2)(1,2) D. (0,3)(0,3)
  59. 59Nurul took 2.5 hours to travel at a constant speed from Town A to B. On her journey back, she increased her constant spe…
  60. 60直线y=x+3与y轴的交点坐标是 ．