![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
Draw a straight line y = - 2 / 3x + 7 / 3 in the rectangular coordinate system. If the line y = x-k intersects with it in the fourth quadrant, find the value range of K
-2/7
Draw a straight line y = - 2 / 3x + 7 / 3 in the rectangular coordinate system. If the line y = x-k intersects with it in the fourth quadrant, find the value range of K
We get x = (3K + 7) / 5, y = (- 2K + 7) / 5
In Cartesian coordinates, if the vertical and horizontal coordinates of a point are all integers, then the point is called the integral point. Let K be an integer. When the intersection of the line y = X-2 and y = KX + k is the integral point, the value of K can be taken as ()
A. Four B. five C. six D. seven
① When k = 0, y = KX + k = 0, that is the x-axis, then the intersection of the line y = X-2 and the x-axis is (2.0), which satisfies the meaning of the problem, ｜ k = 0. ② when k ≠ 0, y = x − 2Y = KX + K, ｜ X-2 = KX + K, ｜ (k-1) x = - (K + 2), ∵ K, X are integers, K ≠ 1, K ≠ 0, ｜ x = − (K + 2) k − 1 = - 1-3k − 1 are integers, ｜ K} K} K} K} K} K} K} K} K} K} K
RELATED INFORMATIONS
- 1. A point whose abscissa and ordinate are all integers is called an integral point. Let K be an integer. When the intersection of the line y = x-3 and y = KX + k is an integral point, how many points does K have From x-3 = KX = k to k = (x-3) / (x + 1), in order to further narrow the scope, how to simplify?
- 2. In Cartesian coordinate system, if the ordinates and abscissa of a point are all integers, then the point is called the integral point. Let K be an integer. When the intersection of the line y = x + 2 and y = KX + 4 is the integral point, how many values of K can be taken at most?
- 3. Four points a (0,1) B (2,1) C (3,4) d (- 1,2) in the plane rectangular coordinate system. Can these four points be on the same circle? Why?
- 4. In the plane rectangular coordinate system, the known points a (- 3,0), B (0, - 4), C (0,1) pass through point C and make the intersection axis of the line at point D, so that points D, C, O In the plane rectangular coordinate system, known points a (- 3,0), B (0, - 4), C (0,1) pass through point C and make the intersection axis of the line at point D, so that the triangle with points D, C, O as the vertex is similar to △ AOB, such a line can make () A. One B. two C. four D. eight
- 5. In the plane rectangular coordinate system, if a (2,4), B (2, - 2), C (6, - 2) are known, then the coordinates of the center of the circle passing through a, B, C are______ ．
- 6. Does the origin belong to the axis?
- 7. In the plane rectangular coordinate system, the point whose abscissa and ordinate are integers is called integral point. Let the unit length of the coordinate axis be 1 cm, the integral point P starts from the origin o, and the velocity is 1 cm And point P can only move up or right When point P starts from point O for several seconds, the integral point (10,5) can be obtained
- 8. In the rectangular coordinate system, O is the origin of the coordinate, a (4,3). Find a point B on the coordinate axis, let △ OAB be an isosceles triangle List them one by one
- 9. Take the point (1,0) as the center and 3 as the radius to draw a circle, then the coordinates of the intersection of the circle and the X axis are______ The coordinates of the point of intersection with the y-axis are_________
- 10. As shown in the figure, point B is on line ad, C is the midpoint of line BD, ad = 10, BC = 3. Find the length of line CD and ab
- 11. The graph composed of all points with the solution of equation 3x + y = 5 as coordinates is a straight line () A.y=3x+5 B.y=3x-5 C.y=-3x+5 D.-3x-5
- 12. In the rectangular coordinate system, the origin of the coordinate is O, a (- 2,4), B (4,2) are known. (1) find the area of △ AOB; (2) find the point P on the x-axis to minimize the value of PA + Pb, and find the coordinate of point P
- 13. As shown in the figure, in the rectangular coordinate system, calculate the coordinates of each vertex of the quadrilateral oabc, and calculate the area of the quadrilateral
- 14. In the rectangular coordinate system, O is the origin, and point a (4,12) is the point on the hyperbola y = x / K (x is greater than 0) 1) Finding the value of K (2) Through the point P on the hyperbola, make Pb perpendicular to the x-axis and connect Op (3) Finding the area of RT triangle OPB (4) If one of the distances between point P and x-axis or y-axis is 6, the coordinates of point P are obtained Grade 8 Volume 2 exercise book people's education press 29 questions 10
- 15. It is known that the lengths of the two right angles of a right triangle are a and B respectively, and the lengths of the hypotenuse are C, and a, B and C are all positive integers, where a is a prime. It is proved that 2 (a + B + 1) = (a + 1) & sup2;
- 16. As shown in the figure, △ ABC is an equilateral triangle with side length L, △ BDC is an isosceles triangle with vertex angle ∠ BDC = 120 ° and makes a 60 ° angle with D as the vertex. The two sides of the angle intersect AB at M and AC at n respectively, and connect Mn to form a triangle. Prove that the perimeter of △ amn is equal to 2
- 17. As shown in the figure, in the plane rectangular coordinate system, point O is the coordinate origin, a (- 4,0), B (0,2) C (6,0). The abscissa and ordinate of line AB and CD are the same as that of point D 1 find D coordinate Starting from O, point P moves at a speed of one unit per second along the positive half axis of x-axis at a constant speed. The vertical line passing through point P and the straight line AB CD intersect at two points E and f respectively. Let P move for T seconds and EF length be y (Y > 0). Find the functional relationship between Y and T and write out the value range of T 3 under the condition of 2, is there a point Q on the straight line CD such that △ bpq is an isosceles right triangle with point P as the right vertex? If so, ask for the coordinates of point Q The graph is the intersection of the first-order function ad through the 123 quadrant and the first-order function DC through the 124 quadrant at the first quadrant (D, a on the negative half axis of X, C on the positive half axis of X, B on the positive half axis of Y)
- 18. As shown in the figure, the parabola y = AX2 + BX + C passes through three points a (- 1,0) B (3,0) C (0,3), the axis of symmetry intersects the parabola at point P, and intersects the straight line BC at point m, connecting Pb 1. Find the analytical formula of the parabola 2. Whether there is a point Q on the parabola, so that the area of △ QMB and △ PMB is equal. If there is, find the coordinate of point Q; if not, explain the reason 3. Whether there is a point R on the parabola on the right side of the symmetry axis in the first quadrant, so that the area of △ rpm and △ RMB is equal. If there is, write the coordinates of point R directly Graph in space
- 19. When a rectangular coordinate system is established with the fixed point of a parabola as the origin and the symmetry axis of the parabola as y, the relation of the parabola can be set as
- 20. In the rectangular coordinate system, the distances from a moving point m (x, 0) on the X axis to two points P (5,5) and Q (1,2) are MP and MQ respectively. Find the minimum value of MP + MQ and the coordinate of point M