Point A is at (-7,-7) and point M is at (-6,-1). Point M is the midpoint of point A and B. What are the coordinates of point B?

The coordinates of point B are (-5, 5).

Given that,

Point A is at (-7,-7), and points M is at (-6,-1).

Point M is the midpoint of points A and B.

We have to determine,

What are the coordinates of point B?

According to the question,

Point A and point B be the ending point of the line segment.

The midpoint formula of a line segment joining these two points is given as:

Then,

Let the coordinates of point B be (x, y),

Point A is at (-7,-7), and points M is at (-6,-1).

Point M is the midpoint of points A and B.

Therefore,

The coordinates of point B is,

And,

Hence, The coordinates of point B are (-5, 5).

For more details refer to the link given below.

link

(-5,5)

Step-by-step explanation:

For point (x1,y1) and (x2,y2) on a coordinate plane ,

coordinate of midpoint is given by (x1+x2)/2, (y1+y2)/2

In the problem

point A(-7,-7)

let point B be (x,y) thus

midpoint point M for AB will be (-7+x)/2, (-7+y)/2

It is given that M is(-6,-1)

hence  (-7+x)/2, (-7+y)/2 will be same as (-6,-1)

Thus,

(-7+x)/2 = -6            and  (-7+y)/2 = -1

=> -7+x = -6*2                =>  -7+y = -1*2

=> -7+x = -12                  => -7+y = -2

=> x = -12+7                   => y = -2+7

=> x = -5                        => y = 5

Thus, coordinates of point B is (x,y) = (-5,5)

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

answer:   (2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

the square root of what number? if you add that, then someone will probably answer the question.