Given that point a (1,2) and point B (5,6) are of length 1, the segment CD moves on the x-axis. When the perimeter of quadrilateral ABCD is the smallest, the coordinate of point D is ()

Given that point a (1,2) and point B (5,6) are of length 1, the segment CD moves on the x-axis. When the perimeter of quadrilateral ABCD is the smallest, the coordinate of point D is ()

Move point B (5,6) one unit to the left to point B ',
Then B 'is (4,6);
Take the symmetric point a '(1, - 2) of point a (1,2) about X axis
Connect a'B ',
Then the intersection of a'b'and x-axis is the required position of point D
Let a'B 'be y = KX + B
Then:
-2=k+b;
6=4k+b.
The solution is as follows
k=8/3,
b=-14/3.
That is to say, the analytical expression of the straight line a'B 'is as follows:
y=(8/3)x-14/3.
Let y = 0,
Then 0 = (8 / 3) x-14 / 3,
x=7/4.
Therefore, when the perimeter of the quadrilateral ABCD is minimum, the coordinate of point D is (7 / 4,0)