As shown in the figure, it is known that the number represented by point a on the number axis is 6, B is a point on the number axis, and ab = 10. Starting from point a, the moving point P moves uniformly to the left along the number axis at the speed of 6 unit lengths per second, and the movement time is t (T > 0) seconds (1) (1) write the number represented by point B on the number axis______ The number represented by point P______ (expressed by an algebraic expression containing T); ② m is the midpoint of AP and N is the midpoint of Pb. Does the length of segment Mn change during the movement of point P? If it changes, please explain the reason; if it doesn't change, please draw a graph and find out the length of line Mn; (2) moving point Q starts from point a and moves left uniformly along the number axis at the speed of 1 unit length per second; moving point R starts from point B and moves left uniformly along the number axis at the speed of 43 unit length per second; if P, Q and R start at the same time, when point P meets point R, it immediately returns to point Q Then, what is the unit length of the journey from the start to the stop of point P? | 数学愛好家 | 数学芸術

As shown in the figure, it is known that the number represented by point a on the number axis is 6, B is a point on the number axis, and ab = 10. Starting from point a, the moving point P moves uniformly to the left along the number axis at the speed of 6 unit lengths per second, and the movement time is t (T > 0) seconds (1) (1) write the number represented by point B on the number axis The number represented by point P (expressed by an algebraic expression containing T); ② m is the midpoint of AP and N is the midpoint of Pb. Does the length of segment Mn change during the movement of point P? If it changes, please explain the reason; if it doesn't change, please draw a graph and find out the length of line Mn; (2) moving point Q starts from point a and moves left uniformly along the number axis at the speed of 1 unit length per second; moving point R starts from point B and moves left uniformly along the number axis at the speed of 43 unit length per second; if P, Q and R start at the same time, when point P meets point R, it immediately returns to point Q Then, what is the unit length of the journey from the start to the stop of point P?

(1) Let the number represented by point B be X. from the meaning of the question, we can get 6-x = 10, x = - 4. The number represented by point B is: - 4, and the number represented by point P is: 6-6t; & nbsp; ② the length of line Mn does not change, which is equal to 5. The reasons are as follows: there are two cases: when point P moves between points a and B: Mn = MP + NP = 12ap + 12bp = 12

If the position of a negative rational number a on the number axis is a, what is the number corresponding to the point farthest from the origin among the points d > o which are D units away from a on the number axis

The number corresponding to the point farthest from the origin is: A-D
There are two points with distance d from a, one is on the right side of a (near the origin), the other is on the left side of a (far from the origin)
The one on the right is a + D, and the one on the left is A-D
Obviously, the one far from the origin is the A-D on the left
Draw a number axis to see clearly

The point corresponding to a negative rational number a on the number axis is a. then, among the points D units (d > 0) away from a on the number axis, the number corresponding to the point farthest from the origin

A is to the left of the origin
The point farthest from the origin should be to the left of A
So it's A-D

A negative rational number a, what is the number corresponding to the midpoint of D units (D is greater than 0) on the number axis and the point farthest from the origin?

If the position of a negative rational number a on the number axis is a, what is the number corresponding to the point farthest from the origin among the points corresponding to D units [D greater than zero] of a on the number axis?

a-d
Because there are two points on the number axis corresponding to D units [D is greater than zero], (A-D) and (a + D)
The point (A-D) is on the left side of a and farthest from the origin

When the three ABC points on the number axis do not coincide with each other, their position relations have six different forms,
There are several cases where AB = ob-oa and ab vector absolute value = ob vector absolute value OA vector absolute value hold simultaneously

There is only one, that is, OB vector and OA vector in the same direction, draw out to understand ~!

A, B, C and the three points on the number axis represent - 7, - 3 and 4 respectively, then the sum of the distances from these three points to the origin is?

Namely:
|-7|+|-3|+|4|=7+3+4=14

If the three points A.B.C on the number axis represent - 3.1.2 respectively, the sum of the distances from the three points to the origin is

|-3|+|1|+|2|=6

If the distance between point a and the origin on the number axis is 4, and the distance between point B and the origin is 7, then the distance between a and B is ()

A may be on the left or right side of the origin, and so is B
If a is 4 and B is 7, the distance between two points is 3
If a is 4 and B is - 7, the distance between two points is 11
If a is - 4 and B is 7, the distance between two points is 11
If a is - 4 and B is - 7, the distance between two points is 3

1. If points a and B are on the number axis, their corresponding numbers are 3x + 2 and 1-2x respectively, and the distances from points a and B to the origin are equal, the value of X can be obtained
2. The sum of 3 (X-2) and 2 (2 + x) is 13
3. If the value of x ^ 2 + 2x is 6, then the value of 3x ^ 2 + 6x is

1
A. The distance between B and the origin is | 3x + 2 | and | 1-2x, respectively|
|3x + 2 | = | 1-2x | square
9x²+12x+4=4x²-4x+1
5x²+16x+3=0
(5x+1)(x+3)=0
X = - 3 or x = - 1 / 5
two
3(x-2)+2(2+x)=13
3x-6+4+2x=13
5x=15
x=3
When x = 3, their sum is 13
three
x^2+2x=6
3x^2+6x
=3(x^2+2x)
=3*6
=18