91影视

The diagram is:

Here, A and B have coordinated a and b, with $b>a$, and the midpoint M of $\stackrel{炉}{AB}$has coordinate x.

Statement 1 is A, M, and B have coordinates a, x, and b respectively; $b>a$.

The statement is already given in the question.

Therefore, the reason for statement 1 is 鈥淕iven information鈥�.

Considering the figure,

Points a, x and b are aligned in such a way that the distance between either of A, N and B equals the absolute value of the difference of coordinates.

Therefore, the 鈥渞uler angle postulate鈥� is used to prove statement 2. This is accepted without any proof.

In the question, it is given that M is the midpoint of $\stackrel{炉}{AB}$.

Therefore, the reason for statement 3 is 鈥淕iven information鈥�.

The midpoint theorem states that if M is the midpoint of $\stackrel{炉}{AB}$, then, $AM=\frac{1}{2}MB$or $MB=\frac{1}{2}AB$which gives $AM=MB$.

Therefore, the reason for statement 4 is 鈥淢idpoint theorem鈥�.

Now, consider step 2 and step 4, substitute $AM=x鈭�a$and $MB=b鈭�x$in $AM=MB$, which gives $x鈭�a=b鈭�x$.

Therefore, the reason for statement 5 is 鈥淪ubstitution Property (Step 2 and Step 4).

Consider step 5,

$\begin{array}{c}x鈭�a=b鈭�x\\ 2x=a+b\end{array}$

Therefore, the reason for step 6 is 鈥淎ddition Property from algebra鈥�.

The division property from algebra states that if $a=b$, then $\frac{a}{c}=\frac{b}{c}$.

In step 6,

$2x=a+b$

Divide $2x=a+b$by 2 on both sides to get,

$x=\frac{a+b}{2}$

Therefore, the reason for statement 6 is 鈥淒ivision Property of algebra鈥�.

The complete table stating the reasons for each statement to prove $x=\frac{a+b}{2}$is: