Math topic中文

Length line segment

finding the length of a line segment given the coordinates of its end points

Practice questions

  1. 1The curve CC has equation y=x2+x+3x−2y = \frac{x^2 + x + 3}{x - 2}. Without using a calculator, find the set of values that yy…
  2. 2The points A, B, C, D and E are shown in the diagram below such that ABC and AED are straight lines and BE = 8\sqrt{8}…
  3. 3已知两定点M(0,1)M(0,1)，N(1,2)N(1,2)，平面内一动点PP到MM的距离与PP到NN的距离之比为2 \sqrt {2}，直线y=kx−1y=kx-1与点PP的轨迹交于AA，BB两点． (…
  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已知圆的方程(x−2)2+y2=1{{(x-2)}^{2}}+{{y}^{2}}=1，过圆外一点P(3,4)P\left(3,4\right) 作一条直线与圆交于A,BA,B两点，那么PA→⋅PB→=\overrightarrow{PA}\cdot \overrightarrow{PB}=…
  6. 6In 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…
  7. 7从点P(3,−1)P(3,-1)向圆x2+y2−4y−5=0x^{2}+y^{2}-4y-5=0作切线PT(TPT(T为切点))，则∣PT∣|PT|等于()(\quad) A. 5                                           5\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: …
  8. 8A, B and C are points (6, 10), (6,6) and (q, 2) respectively. The area of triangle ABC is 16 square units. Show that q =…
  9. 9已知过点P(1,32)P(1,\dfrac{3}{2})的曲线CC的方程为(x−1)2+y2+(x+1)2+y2=2a.(Ⅰ)\sqrt{{{(x-1)}^{2}}+{{y}^{2}}}+\sqrt{{{(x+1)}^{2}}+{{y}^{2}}}=2a.(Ⅰ)求曲线CC的标准…
  10. 10In the diagram, the points P, Q and R have coordinates (9, -3), (6,1) and (18, -3) respectively. Find the length of PQ.…
  11. 11ABCD 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}…
  12. 12直线ll：kx−y+1=0kx-y+1=0被圆x2+y2−4y=0x^{2}+y^{2}-4y=0截得的最短弦长为()() A. 232 \sqrt {3} B. 33 C. 222 \sqrt {2} D. 22
  13. 13A 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…
  14. 14The 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…
  15. 15直线y=−xy=-x与直线y=x+2y=x+2与xx轴围成的三角形的面积为___.
  16. 16P 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…
  17. 17已知直线ll：kx+y−2=0(k∈R)kx+y-2=0(k∈R)是圆CC：x2+y2−6x+2y+6=0x ^{2} +y ^{2} -6x+2y+6=0的一条对称轴，过点A(0,k)A(0 , k)作圆CC的一条切线，切点为BB，则线段ABAB的长度为…
  18. 18Given that the coordinates of point A is (−2,11)(-2,11) and point B is (5,−11)(5,-11). Find length ABAB. Answer ... equation of th…
  19. 19已知直线AB∥x轴，若点A（-2，3），且A，B两点间距为3，则B点坐标为（ ） A. （1，3） B. （-5，3）或（1，3） C. （-2，6） D. （-2，6）或（-2，1）
  20. 20The triangle with vertices A (2, 5), B (−2, −3) and C (2, −2) is shown in the diagram below. Find (a) the area of triang…
  21. 21The diagram shows two congruent isosceles triangles, PQS and RSQ. PQ and RS are parallel to the x-axis. Write down the c…
  22. 22直线x+2y−6=0x+2y-6=0平分圆CC：x2−4x+y2−2by+3+b2=0x^{2}-4x+y^{2}-2by+3+b^{2}=0的周长，过点P(−1,−b)P(-1,-b)作圆CC的一条切线，切点为QQ，则∣PQ∣=()|PQ|=(\quad) A. 55…
  23. 23The diagram shows a trapezium in which ADAD is parallel to BCBC and angle ADC=ADC = angle BCD=90∘BCD = 90^\circ. The points BB…
  24. 24P is the point (3, −1) and Q is the point (−5, 5). Find ∣PQ∣|PQ|. Answer ∣PQ∣|PQ| = ... units The line PQ intersects the x-a…
  25. 25A is the point (1,−4)(1, -4) and B is the point (−7,−2).(-7, -2). The point C is the result of the translation of point B by the c…
  26. 26PQR is a triangle. PQ→=(2−3)\overrightarrow{PQ}=\begin{pmatrix}2\\-3\end{pmatrix}, PR→=(−39)\overrightarrow{PR}=\begin{pmatrix}-3\\9\end{pmatrix}…
  27. 27The point A is (0,7) and the point B is (6,9). Express AB→\overrightarrow{AB} as a column vector. The equation of AB is x…
  28. 28The position vector of point Q is (−7−3)\begin{pmatrix}-7\\-3\end{pmatrix} and the position vector of point R is (51)\begin{pmatrix}5\\1\end{pmatrix}…
  29. 29The figure shows ΔABC. May said that the line AC intersect the y axis at 3.2. Show how you would check if she is correct…
  30. 30已知1∣sin⁡ α∣=−1sin⁡ α\dfrac{1}{|\sin \:α|} =- \dfrac{1}{\sin \:α}，且lg⁡(cos⁡ α)\lg (\cos \:α)有意义． (1)试判断角αα所在的象限． (2)若角αα的终边上一点是M(35,m)M( \dfrac{3}{5} , m)…
  31. 31In the diagram, C is the point (30,15), A is a point on the y-axis and B is a point on the x-axis. Given that the equati…
  32. 32已知以C1C_{1}为圆心的圆C1C_{1}：(x−6)2+(y−7)2=25.(x-6)^{2}+(y-7)^{2}=25.及其上一点A(2,4)A(2,4)． (1)设圆C2C_{2}与xx轴相切，与圆C1C_{1}外切，且圆心C2C_{2}…
  33. 33PP为椭圆x216+y24=1 \dfrac {x^{2}}{16}+ \dfrac {y^{2}}{4}=1上一点，Q(2,0)Q(2,0)，则线段PQPQ长度的最小值为 ___ ．
  34. 34Find the area of the smallest circle passing through the points (2,4) and (5,1). Express your answer in terms of π\pi.…
  35. 35Points P, Q and R have coordinates (1,1)(1, 1), (5,11)(5, 11) and (9,1)(9, 1) respectively. M is the midpoint of QR. Find the coor…
  36. 36The line 3x−5y=103x - 5y = 10 passes through the point A at (5,1)(5, 1) and cuts the y-axis at point B. Write down the gradient o…
  37. 37坐标系中M（-3，2），N（3，2）之间距离是 ．
  38. 38The distance between the points M (k, 7) and N (9, k) is 20\sqrt{20} units. Given that k > 10, find the value of k. Answ…
  39. 39在直角坐标系xOyxOy中，直线ll的参数方程为{x=23−32ty=12t(t \begin{cases} x=2 \sqrt {3}- \dfrac { \sqrt {3}}{2}t \\ y= \dfrac {1}{2}t\end{cases}(t为…
  40. 40C is the point (−9,1)(-9,1) and D is the point (7,4)(7,4). CE→=(−28).\overrightarrow{CE} = \begin{pmatrix} -2 \\ 8 \end{pmatrix}. Calcu…
  41. 41The diagram shows a sketch of the graph of y=−10+2xy = -10 + 2x. The line crosses the axes at P and Q. Find the coordinates of…
  42. 42抛物线y=2(x−3)(x+2)y=2(x-3)(x+2)在xx轴上截得的线段长度为()(\quad) A. 11 B. 22 C. 33 D. 55
  43. 43A, B, C and D are four points such that the coordinates of A and C are (4,2) and (10,−34) respectively. AB→=(−9−12)\overrightarrow{AB}=\begin{pmatrix}-9\\-12\end{pmatrix}…
  44. 44ABCD is a parallelogram. Point A lies on the y-axis and coordinates of D is (6, -1). AC is a horizontal line and gradien…