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If the line L moves 3 units in the negative direction of x-axis and 1 unit in the positive direction of y-axis, then it returns to its original position, then the slope of line L is () A. −13B. -3C. 13D. 3
Let the equation of the straight line l be y = KX + B. according to the translation of the meaning of the problem, we can get y = K (x + 3) + B + 1, that is, y = KX + 3K + B + 1, then KX + B = KX + 3K + B + 1, and the solution is k = - 13
If the line L moves three units to the left along the x-axis, and then one unit up along the y-axis, and returns to the original position, then the slope of the line l will decrease______ ．
Let the equation of the line l be y = KX + B, then y = KX + B translates 3 units to the left along the X axis, y = K (x + 3) + B translates 1 unit up along the Y axis, y = KX + 3K + B + 1. Because it returns to the original position after two translation transformations, there must be 3K + B + 1 = B, and the solution is k = -13
If point P (- 2, a), q (B, 3) and PQ are parallel to y axis, then a=________ ,b=_________ .
a=-3,b=2
If P (- 2, a) Q (B, 3) and PQ are parallel to X axis, then a, B
PQ is parallel to X axis, so the ordinates of PQ are equal, a = 3, B is any number not equal to - 2
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- 1. The line L passing through the left focus F of the ellipse x ^ 2 / 9 + y ^ 2 = 1 intersects the ellipse at P and Q. if the distance between P and Q is equal to the length of the minor axis of the ellipse, the inclination angle of the line L is calculated Please attach the solution,
- 2. If P is on the image of curve y = LNX, q is on the line y = x, and PQ ‖ Y axis, then the minimum distance from P to the line y = x is? And the minimum value of PQ is?
- 3. Given that point P is on the straight line passing through points B (0,2) and C (4,0), and the ordinate is - 1, point q is on the image of y = 3 / x, if PQ / / Y axis, the coordinates of point q are obtained Well, you should be right. Don't answer indiscriminately
- 4. As shown in the figure, angle AOB = 30 degrees, Op bisects angle AOB, PD is parallel to OA, intersection ob at point D, PE is perpendicular to OA at point E, if od = 5cm, PE length is calculated Help. School is about to start.
- 5. In the coordinate system, the distance between P (2, - 2) and Q (2,4) is equal to______ The coordinates of the midpoint of the segment PQ are______ ．
- 6. Point a is on the x-axis, on the left side of the origin, 4 units from the origin, then the coordinate of this point is?
- 7. Given p (3, - 2), q (m, 2m-1) and PQ ⊥ X axis, then the coordinates of Q point are____ . (100 points for correct answers)
- 8. Let p be on the x-axis, Q be on the y-axis, m (- 1,2) be the midpoint of the segment PQ, / PQ / be equal to
- 9. If M (2,1) is the midpoint of PQ, then the equation of this line is
- 10. Reason for filling: because C is the midpoint of line segment AB, AC = half AB () because MP = MQ. And point m is on line segment PQ, so m is the midpoint of line segment PQ ()
- 11. In the plane rectangular coordinate system, the image of a linear function passes through the point a (0,4) B (2,0) (2) to translate the line AB to the left, if the translated line intersects the X axis At point C, and AC = BC, find the coordinates of point C and the expression of the line after translation
- 12. In the plane rectangular coordinate system, the point P of a (0,1) B (2,0) C (4,3) is known to be on the coordinate axis, and the area of triangle ABP and ABC is equal
- 13. If point a (3x + 4,5-2x) is on the bisector of the second and fourth quadrants, find the coordinates of point a
- 14. If point m (3a-9,40-2a) is in the second quadrant and the distance from point m to X axis is equal, try to find the coordinates of point M
- 15. If the point a (2m + 1,3-m) is symmetric about X axis in the fourth quadrant, then the value range of M is_______
- 16. As shown in the figure, the position of right angled trapezoid oabc in the plane rectangular coordinate system is as follows: ab ∥ OC, B (5,3), ab = BC. D (x, 0) is the moving point on OC (not coincident with O and C), DP ⊥ X axis intersects PC at point P, connecting Pb (1) The coordinates of point C are - (2) (1) as shown in figure (1), use the algebraic expression of X to represent the coordinates of point P, and find the value of X when △ PBC becomes a right triangle ② When point P is the intersection of trapezoidal diagonal AC and Bo (as shown in Figure 2), find the value of X
- 17. Draw the following points a (2,1), B (0,1), C (- 4, - 4), D (6, - 4) in the plane rectangular coordinate system, and connect them with line segments to form a quadrilateral ABCD (1) What special quadrilateral is ABCD? A:___ (2) Find a point P in the quadrilateral ABCD so that △ APB, △ BPC, △ CPD, △ APD are isosceles triangles, and request the coordinates of point P
- 18. In the plane rectangular coordinate system, the following points a (2,1) B (0,1) C (- 2,3), D (4,3) are described, and each point is connected by line segments to form a quadrilateral ABCD 1. What special figure is quadrilateral ABCD? 2. Find a point P in the plane of the quadrilateral ABCD so that △ APB, △ BPC, △ CPD, △ APD are isosceles triangles. Please write the coordinates of point P
- 19. In the plane rectangular coordinate system, point a (0,4) B (3,4) C (6,0), moving point P starts from point a and moves downward on the y-axis at a speed of 1 unit / second Starting from point C, the moving point Q moves to the left on the x-axis at a speed of 2 units per second, passing through point P as RP, perpendicular to the y-axis, intersecting ob with R, connecting RQ. When point P coincides with point O, both moving points stop moving. Let the time of motion be T seconds. (1) if t = 1, find the coordinates of point R; (2) if 3
- 20. Given the point a (- 5,3), point B (- 3,5), point C on the x-axis and point D on the y-axis in the plane rectangular coordinate system, which is connected with ABCD, what is the minimum circumference of rectangular ABCD