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

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

(1) If we bring the coordinates of point P into y = K / x, we get K-2 = K / K, so k = 3 (2) because P is on y = K / x, so Mn = k; because OP = 2, so √ (m ^ 2 + n ^ 2) = 2, that is, m ^ 2 + n ^ 2 = 4 (M + n) ^ 2-2mn = 4; 2K ^ 2-2k = 4; k = 2 or K = - 1, because the inverse proportional function y = K / X satisfies: when x > 0, y is with X

As shown in the figure, in the plane rectangular coordinate system, the point P (x, y) is the point on the line y = - x + 6 in the first quadrant, and the area of point a (5,0), △ Pao is S. (1) As shown in the figure, in the plane rectangular coordinate system, the point P (x, y) is the point on the line y = 6-x in the first quadrant, and the area of point a (4,0) and △ Pao is s (1) Find the function relation between S and X, and write the value of X (2) What function of Y is s? What is the range of independent variable y? (3) Find the function relation of s rain x, and write the value range of independent variable x

1、S=2Y=2(6-X)=-2X+12,0＜X＜6
2、0＜Y＜6
3、S=-2X+12（0＜X＜6）

In the plane rectangular coordinate axis, the point P (x, y) is the point on the first quadrant line y = - x + 6, and the point a (5,0) O is the coordinate origin, and the area of triangle Pao is assumed

Is it area?
1.x≠6
2. When x < 6, s △ Pao = 5 * (1 / 2) * y = (5 / 2) y = (- 2 / 5) x + 12 / 5
3. When x > 6, s △ Pao = - (5 / 2) y = (2 / 5) X-12 / 5

The point P (x, y) is the point on the straight line y = - x + 6 in the first quadrant, and the point a (5,0) O is the coordinate origin, and the area of triangle Pao is s. find the functional relationship between S and X Point P (x, y) is the point on the line y = - x + 6 in the first quadrant, point a is (5, 0), O is the coordinate origin, and the area of triangle Pao is s. To find the function relation between S and X, who can tell me why s = 15-2 / 5x

Because point P is on a straight line, let the abscissa of point p be x and the ordinate be - x + 6
Because point a is on the x-axis, OA is the bottom edge of △ POA, and the ordinate of point P is the height of △ OPA
The area of triangle is bottom × height × 1 / 2
S=5•(-x+6)•1/2
s=15-2/5x

As shown in the figure, in the plane rectangular coordinate system, △ ABC is a right triangle, ∠ ACB = 90 ° and the coordinates of points a and C are respectively A（-3,0）,C（1,0）,tan∠BAC= 34． (1) Find the coordinates of point B of a and B; (2) Find a point D on the x-axis and connect BD so that △ ADB is similar to △ ABC (excluding congruence), and calculate the coordinates of point D; (3) Under the condition of (2), if P and Q are the moving points on AB and ad respectively, connect PQ and let AP = DQ = M. ask whether there is such m to make △ Apq similar to △ ADB. If there is, the m value requested; if not, please explain the reason To complete the process ah! To speed, I 1 second best, efficiency~

Obviously, AC = 4, BC = AC x Tan ∠ BAC = 136, so point B is (1136) or (1, - 136). It is obvious that the function expression of the line passing through point a and B is y = 34 (x + 3) or y = - 34 (x + 3) (2) a point D on the X axis, so that △ ADB is similar to △ ABC. Obviously, BC is the height on the right triangle abd, BC ^ 2 = acxcd, CD = 4624, and the point D is (462

As shown in the figure, in the plane rectangular coordinate system, △ ABC is a right triangle, ∠ ACB = 90 ° and the coordinates of points a and C are respectively a (- 3,0), C（1,0）,tan∠BAC= 3/4 (1) Find the coordinates of point B of a and B; (2) Find a point D on the x-axis and connect BD so that △ ADB is similar to △ ABC (excluding congruence), and calculate the coordinates of point D; (3) Under the condition of (2), if P and Q are the moving points on AB and ad respectively, connect PQ and let AP = DQ = M. ask whether there is such m to make △ Apq similar to △ ADB. If there is, the m value requested; if not, please explain the reason

(1) So the coordinates of point B are (1,3) or (1, - 3) because the coordinates of point B can be the first quadrant or the fourth quadrant
(2) : according to the formula of two-point straight line: (Y-Y1) / (x-x1) = (y2-y) / (x2-x), it is concluded that: (Y-Y1) / (x-x1) = (y2-y) / (x2-x)
3X+4Y+9=0,3X-4Y+9=0.
(3) It is known that the triangle ABC is a right triangle, and the point D is on the x-axis, and only the right triangle can be similar to the triangle ABC. Therefore, the triangle abd is a right triangle, and point D cannot coincide with point C. There is only one case, that is, BD is perpendicular to AB, then the coordinates of point D are determined (13 / 4,0

Given both sides of a right triangle, as shown in the figure, known as shown in the figure, △ ABC is a right triangle, ∠ ACB = 90 ° AC = BC, points a and C are on the X axis, the coordinates of point B are (3, m) (M > 0), the intersection point of line AB and Y axis D, the parabola crossing point B with P (1,0) as the vertex, D (1) finds the setting mark of point a (2) the analytic formula of parabola (q is the point between points P and B on the parabola, connect PQ, BQ, and find the maximum area of quadrilateral abqp)

(1) From B (3, m), we can know that OC = 3, BC = m, and △ ABC is an isosceles right triangle,  AC = BC = m, OA = M-3, ? ODA = ∠ oad = 45 °, OD = OA = M-3, then the coordinates of point D are (0, M-3)

In the plane rectangular coordinate system, the image of the first order function y = KX + B passes through (4,2) and intersects with the positive half axis of Y axis at point C, and point B is on the Y axis, and ob = 7, △ ABC area The area of the first order function is 2

From the area of 2, CB = 1, and because ob = 7, we know that point B is (0,7) or (0, - 7), so point C is (0,6) (0,8) (0, - 6) (0, - 8), but point C is on the positive half axis, so C is (0,6) (0,8). The equation obtained by using two-point formula is y = - x + 6 or y = - 1.5x + 8

In the plane Cartesian coordinate system, the points a (- 4,0) and B (2,0) are known. If point C is on the image of the function y = - 2 / 1X + 2 again, and the triangle ABC is straight

Have you learned vector science? Let C coordinate be (x, y) vector AC = (x + 4, y) vector BC = (X-2, y) if the right angle is at C, the equation (x + 4) * (X-2) + y * y = 0, y = - 0.5x + 2 can be brought into the solution to get two answers (the answer is not easy to write, you can calculate it by yourself) if the right angle is at point a, the C coordinate is (- 4,4) if the right angle is at point B, the C coordinate is (2,1)

In the plane rectangular coordinate system, given the points a (- 4,0) and B (2,0), if point C is on the image of the first order function y = - 1 / 2x + 2, and △ ABC is an isosceles triangle, how many C points meet the conditions? See clearly that it is an isosceles triangle, not a right triangle! It is an isosceles triangle! Write the clear process, and the answer is 5,

Do you know, first draw the image of y = - 1 / 2x + 2, then draw a circle with a as the center, AB as the radius, and B as the center of the circle. Because the radius of the circle is equal, as long as the point where the arc intersects with the image of y = - 1 / 2x + 2 is connected, it is an isosceles triangle, and then connect the intersection points of the two circles, which can also form an isosceles triangle, There is a theorem: the distance from any point on the vertical line of a line segment to the end points of both ends of the line segment is equal