Point A is located at (−1,−5). The midpoint of line segment AB is point C(2,3). What are the coordinates of point B ?

The midpoint of a line segment divides the line into equal parts.

The coordinates of B is (5,11)

The given parameters are:

--- the midpoint

The midpoint of a segment is calculated as:

So, we have:

Multiply through  by 2

By comparison:

So, we have:

Hence, the coordinates of B is (5,11)

Read more about midpoints at:

link

For a segment AB, the coordinates of the middle point C are:

xc=(xa+xb)/2,

yc=(ya+yb)/2.

Now, you know points A and C. Thus we get:

xb=2×xc-xa

yb=2×yc-ya

With numerical values:

xb=2×2-(-1)=4+1=5

yb=2×3-(-5)=6+5=11

B(5, 11)

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

step-by-step explanation: