In the plane rectangular coordinate system, the point whose distance to two coordinate axes is 3 has () A. 1 B. 2 C. 3 d. 4

In the plane rectangular coordinate system, the point whose distance to two coordinate axes is 3 has () A. 1 B. 2 C. 3 d. 4

In the plane rectangular coordinate system, there are four points (3,3) or (3, - 3) or (- 3,3) or (- 3, - 3) with the distance of 3 to the two coordinate axes

There is a point P on the coordinate axis, and the distance between it and the point (4, - 3) is 5. Find the point P coordinate. Use the distance formula between two points to solve the process in detail. Thank you. Be quick

If (x, 0)
Then √ [(x-4) 2 + (0 + 3) 2] = 5
(x-4)2=25-9=16
x-4=±4
x=0,x=8
If (0, y)
√[(0-4)2+(y+3)2]=5
(y+3)2=25-16=9
y+3=±3
y=-6,y=0
So it's (0,0), (8,0), (0, - 6)

There is a point P on the coordinate axis, and its distance from point a (4, - 3) is 5

Let p be on the X axis, then the coordinates (x, 0), (x-4) * (x-4) + 3 * 3 = 25 get x = 0 or 8
Let p be on the Y axis, then (0, y), (y + 3) * (y + 3) + 4 * 4 = 25, y = 6 or y = 0
So the coordinates are (0,0) or (8,0) or (0,6)

6. In the plane rectangular coordinate system, it is known that a (1,4), B (3,1), P is a point on the coordinate axis. When the coordinate of P is, the minimum value of AP + BP is taken. What is the minimum value?
(remember to classify)

There are several kinds of answers, but you want the minimum value, so I'll tell you the minimum value directly. The answer is 5 (draw a coordinate to better understand) if you know the coordinates of a and B, do the axisymmetric transformation of point a with the y-axis as the symmetry axis to get a '(- 1,4) connecting a'b. this is the minimum value of AP + BP. Use the Gougu theorem to find the area of △ ABA', which is the root