Your question is poorly formatted; However, the correct question is:
Point A (
3
,
4
) and point M (5.5,0) is the midpoint of point A and point B. Determine the coordinates of B
The coordinates of B is (8,-4)
Step-by-step explanation:
Given
Point A (
3
,
4
)
Point M (5.5,0)
Required
Determine B
Since, M is the midpoint;
We'll solve this question using the following formula;
![M(x,y) = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})](/tpl/images/0737/8624/886b0.png)
Where
and ![(x_1,y_1) = (3,4)](/tpl/images/0737/8624/7c8b1.png)
Substitute values for x, y, x1 and y1 in the above formula;
This gives
![(5.5,0) = (\frac{3 + x_2}{2},\frac{4 + y_2}{2})](/tpl/images/0737/8624/e8bd5.png)
By direct comparison, we have
and ![0 = \frac{4 + y_2}{2}](/tpl/images/0737/8624/08ed4.png)
Solving ![5.5 = \frac{3 + x_2}{2}](/tpl/images/0737/8624/05192.png)
Multiply both sides by 2
![11 = 3 +x_2](/tpl/images/0737/8624/ea2bd.png)
Subtract 3 from both sides
![11- 3 = x_2](/tpl/images/0737/8624/71968.png)
![x_2 = 8](/tpl/images/0737/8624/5082a.png)
Solving ![0 = \frac{4 + y_2}{2}](/tpl/images/0737/8624/08ed4.png)
Multiply both sides by 2
![0 = 4 + y_2](/tpl/images/0737/8624/bb8cb.png)
Subtract 4 from both sides
![0 - 4 = y_2](/tpl/images/0737/8624/8f5f9.png)
![y_2 = -4](/tpl/images/0737/8624/4b266.png)
Hence;
The coordinates of B is (8,-4)