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In the plane rectangular coordinate system, the coordinate of point a is (4,0), the point P is on the straight line y = - x + m, and AP = OP = 4
As shown in the figure, when point P is in the first quadrant, OM = 2, Op = 4. In RT △ OPM, PM = op2-om2 = 42-22 = 23, (4 minutes)
In the plane rectangular coordinate system, the coordinate of point a is (4,0), the point P is on the straight line y = - x + m, and AP = OP = 4
As shown in the figure, when point P is in the first quadrant, OM = 2, Op = 4. In RT △ OPM, PM = op2-om2 = 42-22 = 23, (4 minutes)
In the plane rectangular coordinate system, the coordinate of point a is (4,0), the point P is on the straight line y = - x + m, and AP = OP = 4
As shown in the figure, when point P is in the first quadrant, OM = 2, Op = 4. In RT △ OPM, PM = op2-om2 = 42-22 = 23, (4 minutes)
In the plane rectangular coordinate system, the coordinate of point a is (4,0), P is the point on the straight line x + y = 6 in the first quadrant, and 0 is the origin of the coordinate (1) Set the coordinates of point P as (x, y), and write the relationship between the area s of triangle OPA and y; (2) What is the functional relationship between S and y? Write the value range of the independent variable y in this function relationship; (3) What is the functional relationship between S and X; (4) If x is regarded as a function of S, find the analytic formula of this function and write the range of independent variables in this function
（1）S=OA×y÷2=4×y÷2=2y
（2）S=2y（0
In the plane rectangular coordinate system, the coordinate of point a is (4,0), P is the point on the straight line x + y = 6 in the first quadrant, and O is the coordinate origin 1) Set the coordinates of point P as (x, y), and write the relationship between the area s of △ OPA and y; (2) What is the functional relationship between S and y? Write the range of the independent variable y in the function relationship; (3) What is the functional relationship between S and X; (4) If x is regarded as a function of S, find the analytic formula of this function and write the value range of its independent variable (5) Find the coordinates of P when s = 10 (6) Find a point P on X + y = 6 so that the triangle POA is a triangle with OA as the base
(1) S=2Y （2）0
In the plane rectangular coordinate system, the coordinate of point a is (4,0), point P is a point on the straight line x + y = 6 in the first quadrant, and O is the coordinate origin 1. Let P (x, y), find the area of triangle OPA and the function analytic formula of X 2. When s = 10, find the coordinates of point P 3. Find a point Q on the straight line x + y = 6, so that the triangle QoA is an isosceles triangle with OA as the bottom edge, and write the coordinates of point Q
1. P (x, y), x + y = 6, (0 < x < 6) y = 6 - XS = (1 / 2) the ordinate of OA * P = (1 / 2) * 4 * y = 2Y = 2 (6 - x) 2. S = 2 (6 - x) = 10x = 13
In the plane rectangular coordinate system, the image of the first order function y = - 1 / 2x + 6 intersects x, Y axis at points a and B, and the image of the first order function y = x intersects point C in the first quadrant 1. Coordinates of a, B, C 2. The area of triangle AOC
Mybaitu315's answers are all right. I can help you write down the process simply:
1. Let a (x, 0), B (0, y), C (Z, z)
Substituting the formula y = - 1 / 2x + 6,
have to
0=-1/2x+6,x=12
y=0+6,y=6
z=-1/2z+6,z=4
therefore
A(12,0),B(0,6),C(4,4)
2. You can see that the bottom of the triangle AOC is the X coordinate of a, and the height is the y-axis coordinate of C, so s = 1 / 2 * 12 * 4 = 24
As shown in the figure, in the plane rectangular coordinate system, O is the coordinate origin, and the image of the first order function y = - x + 2 intersects with the X axis at point a, If △ POA is an isosceles triangle, find the coordinates of all points P that meet the conditions
Point P should be at the three points (0,2), (1,1), (2 + root 2, - root 2)
In the plane rectangular coordinate system, O is the origin of the coordinate. Given the first order function y = KX + B (K ≠ 0), the image passes through point a (4,3) and intersects with the X axis at point B, and ob = 3 / 5oa, then the analytic formula of the primary function is - the sooner the better!
4K + B = 3
3/5k+b=0
k=15/17,b=-9/17
The analytical formula is y = 15 / 17x-9 / 17
As shown in the figure, in the plane rectangular coordinate system, ⊙ P and X axis are tangent to origin o, and the straight line parallel to y axis intersects ⊙ P at M and N. if the coordinates of point m are (2, - 1), then the coordinates of point n are () A. （2，-4） B. （2，-4.5） C. （2，-5） D. （2，-5.5）
Ma ⊥ OP is used for crossing point m, and a is for perpendicular foot
Let PM = x, PA = X-1, Ma = 2
Then x2 = (x-1) 2 + 4,
The solution is x = 5
2，
∵OP=PM=5
2，PA=5
2-1=3
2，
/ / op + PA = 4, so the coordinates of point n are (2, - 4)
Therefore, a
RELATED INFORMATIONS
- 1. It is known that O is the origin of the plane rectangular coordinate system. The straight line passing through the point m (- 2,0) and the circle x ^ 2 + y ^ 2 = 1 intersect P and Q If the vector OP * vector OQ = - 1 / 2, find the equation of the line L If the area of the triangle OMP and the triangle OPQ are equal, find the slope of the line L
- 2. As shown in the figure, in the plane rectangular coordinate system, point O is the origin, the diagonal ob of diamond oabc is on the X axis, and the vertex A is in the inverse scale function y = 2 On the image of X, the area of the diamond is______ .
- 3. As shown in the figure, in the plane rectangular coordinate system, the image of quadratic function intersects C at Y axis, a and B at x axis, points a and B are on both sides of the origin The coordinate of a is (- 3,0), Ao = co = 3BO (1) Find this quadratic function expression (2) If the point d (- 2, y) is a point on the parabola, find the area of △ BCD (3) In (2), if point P is a moving point between B and D on the parabola, when P moves to what position, the area of △ BDP is the largest? Find the coordinates of point P and the maximum area of △ BDP!
- 4. In the plane rectangular coordinate system, O is the coordinate origin. The point P (m, n) is on the image of the inverse scale function y = K / X (1) If M = k, n = K-2, find the value of K (2) If M + n = radical 2 K, Op = 2, and the inverse proportional function y = K / X satisfies: when x > 0, y decreases with the increase of X, and the value of K is calculated
- 5. In the plane rectangular coordinate system, the points a (- 4,0) and B (2,0) are known. If the point C is in the first order function y = - 1 On the image of 2x + 2, and △ ABC is a right triangle, then the point C satisfying the condition has () A. 1 B. 2 C. Three D. Four
- 6. It is known, as shown in the figure: in the plane rectangular coordinate system, O is the coordinate origin, the quadrilateral oabc is a rectangle, the coordinates of points a and C are a (10, 0), C (0, 4), respectively; point D is the midpoint of OA, and point P moves on the edge of BC; when △ ODP is an isosceles triangle with waist length of 5, the coordinates of point P are______ .
- 7. It is known that the straight line L is tangent to the circle C: x square + y square + 2x-4y + 4 = 0, and the distance from the origin o to L is 1, and the equation of the straight line L is obtained
- 8. (2006 Yantai) known: on the one variable quadratic equation X2 - (R + R) x + 1 4D2 = 0 has no real root, where R and R are the radii of ⊙ O1, ⊙ O2 respectively, and D is the center distance between the two circles, then the position relationship of ⊙ O1, ⊙ O2 is () A. Exotropism B. Tangency C. Intersection D. Contains
- 9. It is known that a vertex of an ellipse is a (0, - 1) and the focus is on the x-axis. If the distance between the right focus and the root of the line X-Y + 2 is 2 = 0, the distance is 3 Let the ellipse intersect with the straight line y = KX + m and have different two points m n when am = an to find the value range of M
- 10. How many points on the circle x ＾ 2 + y ＾ 2 + 2x + 4y-3 = 0 to the straight line x ＾ y + 1 = 0 is the root sign 2! Although there are online solutions, but I still don't understand! Please explain!
- 11. As shown in the figure, it is known that in the rectangular coordinate system xoy, points a and C are on the positive half axis of the x-axis and y-axis respectively, and the point O is at the coordinate origin. The right angle vertex o of the isosceles right angle triangle OEF is at the origin, e and F are on OA and OC respectively, and OA = 4, OE= 2. Rotate the triangle plate OEF anticlockwise around point O to oe1f1, and connect CF1 and AE1 (1) Verification: △ oae1 ≌ △ ocf1; (2) If the triangle plate OEF rotates anticlockwise around point O, is there a position that makes OE ∥ CF? If yes, request the coordinates of e point; if not, please explain the reason
- 12. As shown in the figure, in the plane rectangular coordinate system, the coordinates of the three vertices of △ ABC are a (2, 3), B (2, 1), C (3, 2) (1) Judge the shape of △ ABC; (2) If △ ABC is rotated one circle along the line of edge AC, the volume of the rotating body is obtained
- 13. In a rectangular coordinate system, a point whose abscissa and ordinate are integers is called a lattice point. Given that the center of a circle is at the origin and its radius is equal to 5, then the grid point on the circle has______ One
- 14. Given that the length of a chord is equal to the radius r, find: (1) The length of the inferior arc to which the string is directed; (2) The area of the bow formed by this chord and minor arc
- 15. Given that ⊙ O1 and ⊙ O2 are circumscribed at point a, the radius of ⊙ O1 is r = 2, and the radius of ⊙ O2 is r = 1, then the circle with radius 4 has () A. 2 B. Four C. Five D. 6
- 16. The function is equal to the root x + 4, and the value range of the independent variable x is
- 17. It is known that m (x, y) is a set of inequalities where x is greater than or equal to 0, less than or equal to root 2, y is less than or equal to 2, and X is less than or equal to root sign 2Y If point a (root 2,1), then z = vector OM, the maximum value of point multiplication vector OA is
- 18. It is known that the distance from point a (2m + 1,3m-5) to the x-axis is twice the distance from the point to the y-axis
- 19. If the chord length of the straight line 2x-y + 1 = 0 and the section circle x? 2 + y? 2 = R? 2 is equal to 5, find the radius of the circle
- 20. In the plane rectangular coordinate system, the distance from the point P (- 3, - 4) to the X axis is () and the distance from the point to the Y axis is