It is known that the image with inverse scale function y = 1 / X and primary function y = 2x-1 has an intersection point a (1, a). Whether there is a point P on the x-axis makes the triangle POA isosceles Triangle? If it exists, find out the coordinates of point P. if not, explain the reason

It is known that the image with inverse scale function y = 1 / X and primary function y = 2x-1 has an intersection point a (1, a). Whether there is a point P on the x-axis makes the triangle POA isosceles Triangle? If it exists, find out the coordinates of point P. if not, explain the reason

A: there is such a point P on the x-axis, so that △ POA is an isosceles triangle. From the question, we can see that a (1,1) is connected with OA, then OA = √ 21) when OA is the waist and point O is the vertex, O is the center of the circle, OA length is the radius of the arc, and there are two intersections with the x-axis, that is, the point P satisfying the condition. The coordinates of the two points are: P1 (√ 2,0), P2 (- 2,0), 2) when OA

As shown in the figure, given that the coordinates of point a are (2,1), O is the origin of coordinates, find a point P on the x-axis, make the triangle AOP isosceles triangle, and write out the coordinates of point P

There is a trap in this problem, that is, the P point may be on the negative axis or on the positive axis
Because the triangle AOP is isosceles triangle, according to the writing habit of isosceles triangle, Ao and op are isosceles
So according to the distance formula between two points, Ao = √ 5 is calculated
If it is on the positive axis, then the coordinates of point P are (√ 5,0)
If it is on the negative axis, the coordinates of point P are (- √ 5,0)

In the plane rectangular coordinate system, O is the coordinate origin, a (1,1) is known, the point P is determined on the x-axis, so that △ AOP is an isosceles triangle, then the number of points P that meet the condition is______ ．

(1) If Ao is the waist, there are two cases: when a is the vertex, P is the intersection of a and the x-axis; when o is the vertex, P is the intersection of O and the x-axis; (2) when OA is the bottom, P is the intersection of the x-axis and the perpendicular of OA. The above four intersections are not coincident Therefore, there are 4 qualified points

In the plane rectangular coordinate system, the straight line y = - 1 / 2x + B intersects the x-axis at point a and the y-axis at two points of point B respectively, and s △ ABO = 4. The analytical formula of the straight line AB is obtained

The line y = (- 1 / 2) x + B intersects the x-axis at point a (2B, 0), and intersects the y-axis at point B (0, b),
∴S△ABO=b^=4,
The analytic formula of the line AB is y = (- 1 / 2) x soil 2