Know a (2,1), B (1,3), find a point P on the x-axis, so that the value of PA + Pb is the minimum, then what is the minimum value?

Know a (2,1), B (1,3), find a point P on the x-axis, so that the value of PA + Pb is the minimum, then what is the minimum value?

B the symmetric point B '(1, - 3) about X axis connects ab', the intersection of ab 'and X axis is point P [Pb = PB', the shortest straight line distance between two points]; P (x, 0), the same straight line slope (2-x): (1-0) = (x-1): [0 - (- 3)] X-1 = 3 (2-x) X-1 = 6-3x4xx = 7x = 7 / 4P (7 / 4,0) the minimum value is | ab '| = √ (2-1) ^ 2 + (1 + 3) ^

Given the point a (1,2) B (- 2,3), find a point P on the x-axis so that PA + PB has a minimum value

The symmetric point B '(- 2, - 3) of B about X axis
The intersection point connecting ab ', ab' and X axis is point P [Pb = PB ', the shortest straight line distance between two points];
P(X,0),
1-X:2-0=X-(-2):0-(-3)
3-3X=2X+4
5X=-1,
X=-1/5
P(-1/5,0)

Given two points a (2,0), B (5,1), and point P is a point on x-axis, the minimum value of PA + Pb is obtained
D.was leaving

A is on the x-axis
So when P and a coincide, it is the smallest
So p (2,0)

Given the points a (1,1), B (2,2) and P on the straight line y = 12x, find the coordinates of point P when | PA | 2 + | Pb | 2 gets the minimum value

Let P (2t, t), then | PA | 2 + | Pb | 2 = (2t-1) 2 + (t-1) 2 + (2t-2) 2 + (T-2) 2 = 10t2-18t + 10. When t = 910, the minimum value of | PA | 2 + | Pb | 2 is obtained. When p (95910) | PA | 2 + | Pb | 2 has the minimum value, the coordinate of P point is (95910)