The corresponding point of the number a on the number axis is to the left of the origin, and | a |=3, then a =______.

The corresponding point of the number a on the number axis is to the left of the origin, and | a |=3, then a =______.

The corresponding point of the number a on the number axis is on the left of the origin, that is, the number is negative, so a=-3.

The number corresponding to A on the number axis is a, the number corresponding to B is b, and satisfies |a-12||b+6|=0, O is the origin, (1) Find the values of a and b, and mark A and B on the number axis. (2) On the number axis, A starts to move to the left at the speed of 3 units per second and B starts to move to the left at the speed of 1 unit per second. At point C, A catches up with B, so what is the corresponding number of point C? (3) If point A does not move, point B still moves to the left at a speed of 1 unit per second, M is the midpoint of line segment OB, N is the midpoint of line segment AB, during the movement of point B, does the length of line segment MN change? If so, explain the reason; if not, find the length.

(1) A-12 b+6|=0,
A-12=0, b+6=0,
Solve to a=12, b=-6,
Represented on the number axis as:

(2) If the time is t seconds, then
3T-t=12+6,
T=9,
The number represented by point C is -6-9=-15;
(3) Point B represents -6-t,
M points represent −3−t
2,
The number represented by point N is 3−t
2,
MN |=|(3−t
2)-(−3−T
2)|=6.