In the plane rectangular coordinate system, the distances from the moving point P to the fixed points a (1,1) and B (5,7) on the x-axis are AP and BP respectively. Then when AP + BP is the minimum, P is calculated Don't use functions and linear equations or analytic expressions, Finding the coordinates of point P

In the plane rectangular coordinate system, the distances from the moving point P to the fixed points a (1,1) and B (5,7) on the x-axis are AP and BP respectively. Then when AP + BP is the minimum, P is calculated Don't use functions and linear equations or analytic expressions, Finding the coordinates of point P

(1) Take a point A1 in the fourth quadrant so that a (1,1) and A1 (1, - 1) are symmetrical about the X axis,
(2) It is the smallest to connect the x-axis of A1B to P, PA + Pb = PA1 + Pb = 4 √ 5
(3) From A1 (1, - 1) B (5,7)
Line A1B: y = 2x-3
When y = 0, x = 3 / 2, P (3 / 2,0)

In the plane rectangular coordinate system, the distances from a moving point P on the x-axis to fixed points a (1,1), B (5,7) are AP and BP respectively. When BP + AP is the minimum, the coordinates of point P are______ Should this problem be finished by drawing or calculating?

In the plane rectangular coordinate system, the distances from a moving point P of X axis to fixed points a (1,1), B (5,7) are AP and BP respectively, then when BP + AP is the smallest, the coordinate of P point is 3 / 2. Calculation: finding the minimum √ [(x-1) ^ 2 + 1] + √ [(X-5) ^ 2 + 7 * 7] is more complicated. Drawing: a making the symmetrical point a ~ (1, - 1) about X axis, connecting a ~ B, intersecting X axis

In the plane rectangular coordinate system, the distances from the moving point P on the X axis to the fixed points a (1,1) B (6,4) are AP and BP respectively
When AP + BP is minimum, the coordinates of point P are obtained
Don't use straight-line equations,

The symmetric point of point a (1,1) about X axis is a '(1, - 1)
Let the analytic expression of a ′ B be y = KX + B,
Substituting the coordinates of a '(1, - 1) and B (6,4), we get
{k+b=-1
6k+b=4
The solution is: {k = 1
b=-2
The analytic expression of the straight line a ′ B is y = X-2
Let y = 0, X-2 = 0, x = 2
When AP + BP is minimum, the coordinates of point P are (2,0)

In the plane rectangular coordinate system, the distances from a moving point P on the X axis to the fixed points a (1,1). B (5,1) are AP and BP respectively. When BP + AP is the minimum, the coordinates of point P are__

According to the meaning of the title:
The symmetry point of B (5,7) about X axis is (5, - 7)
The line passing (1,1) and (5, - 7) is y = KX + B
∴{1=k+b-7=5k+b,
∴{k=-2b=3
∴y=-2x+3
Let y = 0, then x = 3 / 2
So the coordinate of P point is (3 / 2,0)