![](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>)
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
1A (- 1,0) B (3,0) C (0,3) X1 = - 1, X2 = 3, x = 0, y = C = 3x1x2 = C / a = - 3A = - 1x1 + x2 = 2 = - B / AB = 2Y = - x ^ 2 + 2x + 3 symmetry axis X = - B / 2A = (x1 + x2) / 2 = 1, C-B ^ 2 / 4A = 3-4 / (- 4) = 4 vertex P (1,4) straight line BC: Y-3 = [(3-0) / (0-3)] xy = - x + 3x = 1, y = 2m (1,2) P (1,4) 2 through P parallel BC
As shown in the figure, in the plane rectangular coordinate system, point a (- 3,0), B (0,6), C (0,1), D (2,0), find the intersection of line AB and line CD
Reward 10 points! Urgent!
The reward is 100 points. It's wrong~
Let a (- 3,0), B (0,6) be substituted into the analytic expression of the line AB to obtain {- 3k1 + B1 = 0b1 = 6 solution to obtain: {K1 = 2B1 = 6} the analytic expression of the line AB is y = 2x + 6, let the analytic expression of the line CD be y = k2x + B2, and substitute C (0,1), D (2,0) into the analytic expression of the line CD to obtain {B2 = 12k2 + B2 = 0 solution to obtain: {K2 = - ## - 189; B2 = 1} the analytic expression of the line CD is y = k2x + B2
In the plane rectangular coordinate system, the coordinates of points a, B, C and D are shown in Figure 6, and the intersection coordinates of line AB and line CD are obtained
A (- 3,0), B (0,6); C (0,1), D (2,0) so let the analytic expression of AB be y = KX + B, then a is x = - 3, when y = 0, the equation (1) 0 = - 3K + B can be obtained; B is x = 0, when y = 6, the equation (2) 6 = 0 + B can be obtained; from (1) (2) simultaneous equations, k = 2, B = 6 can be obtained, so the analytic expression is y = 2x + 6, similarly, the analytic expression of straight line CD is y = - 1 / 2x + 1, and the two analytic expressions can be obtained as the equations, x = - 2, The value of y = 2 is the intersection coordinate (- 2,2)
As shown in the figure, in the plane rectangular coordinate system, point a (- 3,0), B (0,6), C (0,1), D (2,0), find the intersection of line AB and line CD
Write AB linear expression: (y-6) = 2x; CD expression: y = - 1 / 2 (X-2): simultaneously get x = - 2, y = 2
The answer is (- 2,2)
RELATED INFORMATIONS
- 1. 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)
- 2. 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
- 3. 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;
- 4. 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
- 5. 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
- 6. 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
- 7. 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
- 8. 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
- 9. 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?
- 10. 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?
- 11. 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
- 12. 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
- 13. Known: in the plane rectangular coordinate system, m (0,1), n (2,2), take a point P on the x-axis to minimize the value of PM + PN, then what is the coordinate of point P A (3 / 2, 0) B (3 / 2, 0) C (0, 3 / 2) d (2 / 3, 0)
- 14. In Cartesian coordinate system, point m (- 4,2), point n (2, - 6), point P are on Y axis, and PM = PN, then the coordinates of point P are obtained
- 15. Given the square oabc with side length of 2, in the rectangular coordinate system, the angle between OA and Y axis is 30 degrees, find the coordinates of point a, point B and point C
- 16. It is known that the oabc of a square whose side length is 1 is in the rectangular coordinate system, the two points a and B are in the first quadrant, and the angle between OA and X axis is 30 degrees
- 17. It is known that in the plane rectangular coordinate system xoy, the image of quadratic function y = x2-bx + C (b > 0) passes through point a (- 1, b) and intersects with y axis at point B, and the cotangent value of ∠ ABO is 3. (1) find the coordinates of point B; (2) find the analytic expression of this function; (3) if the top point of this function image is C, prove: ∠ ACB = ∠ abo
- 18. As shown in the figure, it is known that BF is perpendicular to AC, CE is perpendicular to AB, BF and CF intersect at D, and BD = CD
- 19. Given the diameter ab of circle O, perpendicular to the chord CD at point E, connect CO and extend the intersection ad at point F. if CF is perpendicular to ad, ab = 2, find the length of CD process CF is not the center of the circle
- 20. Thank you very much: in the circle O, the chord AB intersects the chord CD, and ab = CD