Given the points A(-2,5) and B(4,7)determine the middle point of AB.
The mid point between the points (x1, y1) and ( x2, y2) is given by [(x1 + x2)/2 , (y1 + y2)/2]
Here we have the points A(-2 , 5) and B( 4 , 7)
The middle point has the coordinates [( -2+4)/2 , (5+7)/2]
=> ( 2/2 , 12/2)
=> (1 , 6)
The mid point of AB is ( 1 , 6)
We'll begin by recalling the midpoint formula:
M = (xM ; yM)
xM = (x1 + x2)/2
yM = (y1+y2)/2
x1,x2,y1,y2 are the coordinates of the given points A and B. Since the coordinates are added, it doesn't matter which point is the first one, whose coordinates are x1 and y1, and which point is the second one.
We'll identify x1 = -2, x2 = 4, y1 = 5 and y2 = 7
Now, we'll calculate the coordinates of the midpoint:
xM = (-2+4)/2
xM = 1
yM = (5+7)/2
yM = 6
The coordinates of the midpoint M of the segment AB are: M(1 ; 6).