# If C is the midpoint of the degment AB such that C(2,3) and A(-4,-1) find B.

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Given that the point C(2,3) is a midpoint of the line segment AB such that A(-4,-1)

We need to find the other end of the line segment.

We will use the midpoint formula to find the coordinates of the point B.

We know that:

Cx = ( Ax + Bx)/2

==> 2 = (-4 + Bx)/2

==> -4+Bx = 4

We will add 4

==> Bx = 8

Now we will calculate the y-coordinate.

==> Cy = (Ay+By)/2

==> 3 = (-1+By)/2

==> -1 + By = 6

==> By = 7

**Then the point B is:**

**B ( 8, 7)**

It is given that C is the midpoint of A and B.

The coordinates of C are (2,3) and that of A are ( -4, -1)

Let B have the coordinates (x , y)

As C is the midpoint of A and B, we have

(x + -4)/2 = 2

=> x - 4 = 4

=> x = 8

(y + - 1)/2 = 3

=> y - 1 = 6

=> y = 7

**So the point B is ( 8 , 7)**

C is the mid point of AB.

Therefore the coordinates of C are given by:

(xC , yC) = C(2,3).

xC = (xA+xB)/2 by mid point formula.

2 = (-4+xB)/2.

=> 2*2 = -4+xB.

=> 4+4 = xB . So xB = 8.

Similarly, yC = (yA+yB)/2 by mid point formula.

3 = (-1+yB)/2.

=> 3*2 = -1+yB.

=> 6+1 = yB. So yB = 7.

Therefore the coordinates of B = (xB, yB) = (8, 7).