Answer:
The coordinates of point B is
( 7 , 3)
Step-by-step explanation:
The midpoint M of two endpoints of a line segment can be found by using the formula
[tex]M = ( \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} )[/tex]
where
(x1 , y1) and (x2 , y2) are the points
Let the coordinates of B be ( x , y)
From the question the midpoint is ( 0 , 4) and A is (-7 , 5)
So we have
[tex](0 \: , \: 4) = ( \frac{ - 7 + x}{2} , \: \frac{5 + y}{2} )[/tex]
Next we compare the x and y coordinates of the midpoint to the x and y coordinates on the right hand side to find the missing coordinates
That's we equate them
So we have
For x
[tex]0 = \frac{ - 7 + x}{2} \\ - 7 + x = 0 \\ \\ x = 7[/tex]
For y
[tex]4 = \frac{5 + y}{2} \\ 8 = 5 + y \\ y = 8 - 5 \\ \\ y = 3[/tex]
So we have
x = 7 , y = 3
So the coordinates of point B is
( 7 , 3)
Hope this helps you
