The fifth chapter of the first volume of the eighth grade mathematics is the plane rectangular coordinate system (full mark: 100: 60).
First, multiple-choice questions (3 points for each question, ***24 points)
1. The following coordinates are in the second quadrant ().
A.(2，3) B.(-2，3) C.(-2，-3) D.(2，-3)
2. The point P (-2, -3) is moved to the left by 1 unit length, and then moved up by 3 unit lengths, and the coordinates of the point obtained are ().
A.(-3，0) B.(- 1，6) C.(-3，-6) D.(- 1，0)
3. In the plane rectangular coordinate system xOy, if the coordinate of point A is (-3,3), the coordinate of point B is (2,0), and the area of △ABO is ().
A. 15
4. The following figure shows the distribution map of the main buildings of the Palace Museum drawn by using the plane rectangular coordinate system. If this coordinate system takes the east and north directions as the positive directions of the X axis and the Y axis respectively, then the coordinates of the point representing the Hall of Supreme Harmony are (0,-1), and the coordinates of the point representing the Nine Dragon Wall are (4, 1), which means that the coordinates of the following palace points are correct ().
A. Ren Jing Palace (4,2) B. hall of mental cultivation (-2,3)
C. Baohe Hall (1, 0) D. Wuying Hall (-3.5, -4)
5. One day after dinner, Xiaoming accompanied his mother to go out for a walk from home. The above picture describes the functional relationship between the distance from home s(m) and the walking time t (min) during their walking. The following description is in line with their walking scene ().
A. Starting from home, I went to a bookstore, looked at it for a while and then went home.
B. Starting from home, I went to a bookstore, read for a while, walked for a while, and then went home.
C. Start from home, go straight (without stopping) and then go home.
D. I started from home, walked for a while, went to the bookstore, read a book for a while, walked on for a while, and began to return after 18 minutes.
6. Fill a container with water at a uniform speed, and finally fill the container. In the process of water injection, the variation law of water surface height h with time t is shown in the figure (OABC is a dotted line in the figure), so the shape of the container is ().
7. Xiaomi takes a cruise to the sea to play. The results of radar scanning on the cruise ship are shown in the figure. The distance between every two adjacent circles is l km (the radius of a small circle is l km). If the position of the ship C relative to the cruise ship can be expressed as (0? ,-1.5), which correctly describes the positions of the other two ships A and B in the figure is ().
A. Boat A (60? , 3), B boat (-30? ,2)
B. Boat A (30? , 4), B boat (-60? ,3)
C. Boat A (60? , 3), B boat (-30? ,3)
D. boat A (30? , 3), B boat (-60? ,2)
8. In the plane rectangular coordinate system, Kongming plays chess as follows: the chess pieces start from the origin, move to the right in step 1 unit length, move to the right in step 2 for 2 unit lengths, move up in step 3 for 1 unit length, move to the right in step 4 for 1 unit length, and so on. When n is divided by 3 and the remainder is 1, then go right 1 unit length; When n is divided by 3 and the remainder is 2, walk 2 unit lengths to the right. When step 100 ends, the coordinate of the chess piece position is ().
A.(66，34) B.(67，33) C.( 100，33) D.(99，34)
Fill in the blanks (2 points for each question, 20 points for * * *)
9. If point P (m+5, m+ 1) is on the Y axis of rectangular coordinate system, the coordinates of point P are.
10. As shown in the figure, point A is on the ray OX, and the length of OA is equal to 2 cm. What if OA rotates 30 counterclockwise around point O? To OA 1, then you can use the position of point A 1 (2,30? ). If OA 1 is rotated counterclockwise by 55? To OA2, then the position of point A2 can be represented by (,).
1 1. In the plane rectangular coordinate system, the coordinate of point A is (2, -3). If point A is symmetrical about X axis to get point A', and then point A' is symmetrical about Y axis to get point A ",the coordinates of point A" are.
12. If the coordinates of vertices A, B and C of a square ABCD are (-1, 1), (-1,-1), (1,-/kloc-.
13. As shown in the figure, Xiao Qiang tells Xiaohua that the coordinates of point A and point B in the figure are (-3,5) and (3,5) respectively. Xiaohua just tells the coordinates of point C in the same coordinate system, and the coordinates of point C are.
14. The picture below shows a flight formation of the bomber fleet. If the plane coordinates of the last two bombers are A (-2, 1) and B (-2, -3) respectively, then the plane coordinates of the first bomber C are.
15. In the rectangular coordinate system, it is known that point A (00,2) and point P (x x, 0) are moving points on the X axis. When x=
The length of line segment PA is the smallest, and the minimum value is.
16. As shown in the figure, the coordinates of point A and point B are (2,4) and (6,0) respectively, point P is a point on the X axis, and the area of triangle ABP is 6, so the coordinates of point P are.
17. In the plane rectangular coordinate system, o is the coordinate origin, and the coordinate of point A is (1,) m is a point on the coordinate axis. If △MOA is an isosceles triangle, then the number of points that meet the conditions is m.
18. In the plane rectangular coordinate system, it is stipulated that a triangle should be folded along the X axis first, and then translated to the right twice with the unit length of 1. As shown in the figure, the coordinates of vertices B and C of equilateral triangle △ABC are (-1,-1) and (-3, -65438) respectively.
Iii. Answering questions (***56 points)
19. (6 points in this question) As shown in the figure, point A is represented by (3, 1), and point B is represented by (8,5). What if it is represented by (3, 1)? (3,3)? (5,3)? (5,4)? (8,4)? (8, 5) indicates a road from point A to point B, which stipulates that it can only go up or right from point A to point B. Try to write the other two roads with the above representation to judge whether the distances of these two roads are equal.
20. In the plane rectangular coordinate system, point A (1, 2a+3) is in the first quadrant.
(1) If the distance from point A to the X axis is equal to the distance to the Y axis, find the value of a;
(2) If the distance from point A to the X axis is less than the distance to the Y axis, find the value range of A. 。
2 1. (6 points in this question) Given points O (00,0), A (33,0), point B is on the Y axis, and the area of △OAB is 6, find the coordinates of point B. 。
22. (8 points in this question) As shown in the figure, in △OAB, A (2 2,4) and B (6 6,2) are known, and the area of △OAB is found.
23. (9 points for this question) As shown in the figure, in the plane rectangular coordinate system, point A (-3b,0) is a point on the negative semi-axis of X axis, and point B (00,4b) is a point on the positive semi-axis of Y axis, where b satisfies equation 3(b+ 1)=6.
(1) Find the coordinates of point A and point B. 。
(2) If point C is a point on the negative semi-axis of Y axis and the area of △ABC is 12, find the coordinates of point C. 。
(3) Is there a point P on the X axis that makes the area of △PBC equal to half of the area of △ABC? If it exists, find the coordinates of the corresponding point p; If it does not exist, please explain why.
24. (9 points for this question) Read the following paragraph and then answer this question.
There are two points P 1 (x 1, y 1) and P2 (x2, y2) on the known plane, and the distance between the two points is P 1P2=. When the straight line where two points are located is on the coordinate axis or parallel to the coordinate axis or perpendicular to the coordinate axis, the distance formula between two points can be simplified as or.
(1) Given A (2 2,4) and B (-3,8), try to find the distance between A and B. 。
(2) Assuming that A and B are on the same straight line parallel to the Y axis, the ordinate of point A is 5 and that of point B is-1, try to find the distance between point A and point B. 。
(3) Given that the coordinates of each vertex of a triangle are A (00,6), B (-3,2) and C (33,2), can you determine the shape of this triangle? Please explain the reason.
25. (Question 10) In a plane rectangular coordinate system, a point whose abscissa and ordinate are integers is called the hour. Let the unit length of the coordinate axis be 1 cm, the whole point P starts from the origin O, and the speed is 1 cm/s. If the whole point P only moves to the right or upward, it can reach (0, 1) and (1,0) after moving 1 s; After 2 s of exercise, you can reach (2,0), (1, 1), (0,2). After 3 s of exercise, you can reach (3,0), (2, 1), (1, 2) and (0,3) four whole points.
Please explore and answer the following questions:
(1) How many * * * points can be reached in an hour when p departs from point O for 4 s?
(2) Draw the whole point that the whole point P can reach after 8 s from the O point in the rectangular coordinate system, observe these whole points and tell what their characteristics are in position.
(3) How many seconds can P reach the position of (13,5) after starting from O?
The first volume of the eighth grade mathematics Chapter 5 Reference answers to examination papers in plane rectangular coordinate system I. Multiple choice questions
1.b2.a3.d4.b5.d6.c7.d8.c [Hint: when n=99, it is divisible by 3, and the quotient is 33, * * * 33 units up and 99 units to the right; When n= 100, divided by 3, the remainder is 1. Continue to go right 1 unit length, that is, the coordinate at this time is (100,33)]
Second, fill in the blanks
9.(0,-4) 10.(2,85? ) 1 1.(-2,3) 12.( 1, 1) 13.(- 1,7) 14.0) 17.6 18.( 16， 1+) [Hint: get the coordinates (-2,-1-) of A' (2n-2) from the meaning of the question, and then get the transformation of 1, 2, 3 according to the meaning of the question. When n is an even number, A' (2n-2,-1- )]
Third, answer questions.
19. When the distance is equal, the answer is not unique. Method 1: (3, 1)? (6, 1)? (6,2)? (7,2)? (8,2)? (8,5); Option 2: (3 1)? (3,2)? (3,5)? (4,5)? (7,5)? (8,5); etc
20. (1) ∫ The distance from point A to the X axis is equal to the distance to the Y axis. 2a+3= 1, and the solution is a =-1(2) ∫ The distance from point A is less than the distance from axis X, and point A is in the first quadrant. 2a+3 & lt； 1 and 2a+3 >；; 0，a； - ,? -& lt； a & lt- 1
2 1.S△OAB=？ OA？ OB=6，∫A(3，0)，？ OA=3，？ OB=4，？ The coordinates of point B are (0,4) or (0,4).
22. As shown in the figure, construct a rectangular OCDE. ∫A(2 ^ 2，4)，B(6 ^ 6，2)，？ AE=2，OE=4，OC=6，BC=2，？ AD=6-2=4，BD=4-2=2，？ S△OAB=4？ 6- ? 4? 2- ? 6? 2- ? 2? 4= 10
23.( 1) solve equation 3 (b+ 1)=6, and get b= 1,? A (-3，0)，B (0，4)(2)∫A(-3，0)，？ Oa = 3。 The area of ∵△ ABC is 12, and S△ABC= BC? OA=？ 3? BC= 12，？ BC=8。 ∫B(0，4)，？ OB=4，？ OC=4，？ C (0, -4) (3) exists. The area of △PBC is equal to half the area of △ABC. What is the high OP of BC? The coordinates of point P are (,0) or (-,0).
24.( 1)∫A(2，4)，B (-3，-8)，？ AB= = 13, that is, the distance between two points A and B is 13 (2) ∵ A and B are on a straight line parallel to the Y axis, the ordinate of point A is 5, and the ordinate of point B is-1. AB= =6, that is, the distance between two points A and B is 6(3)∫ The coordinates of each vertex of the triangle are A (00,6), B (-3,2), C (33,2),? AB=5，BC=6，AC=5，？ AB=AC，？ △ABC is an isosceles triangle
25. The points that can be reached after (1) 4s are (4,0), (1, 3), (2,2), (3,1), (0,4) and * * 5 (2). The whole point P can reach the position of (13,5) after starting from point O18 s.