Study Midpoint Formula

A midpoint formula is a mathematical form halfway between two stellar bodies that tells an interpretative picture for the individual. Direct and indirect are the types of mid point. Sometimes you need to find the point that exactly between two other points. For other instance, you might need to find a line that bisects in a given line segment. These middle point is called the "midpoint".



Discussion on study midpoint formula


If the co-ordinates of the end points of a segment are (x1, y1) and (x2, y2), then the co-ordinates of the mid point of this segment is given by the mid point formula :

M=[(x1+x2)/2,(y1+y2)/2]


Examples on study midpoint formula


Study midpoint formula Example 1:

To find the mid point formula between A(1,2)and B(3,6)

solution:
Let the coordinates of  A(1,2) andB(3,6)

=((1+3)/2,(2+6)/2)

=(4/2,8/2)

=(2,4)

Study midpoint formula Example 2:

M(3, 8) is the midpoint formula of the line AB. B has the coordinates (-2, 3), Find the coordinates of A.

Solution:
Let the coordinates of B be (x, y)

[(-2+x)/2,(3-y)/2]=(3,8)

[(-2+x)/2]=3==>x=8

[(3+y)/2]=3==>x=13

Coordinates of B = (8, 13)

Study midpoint formula Example 3:

What is the midpoint formula between the points (5, 6) and (– 12, 40)?

Solution:

(m1,m2)=((5+(-12)/2),(6+40)/2)

=(-7/2,46/2)

=(-7/2,23)

Study midpoint formula Example 4:

If the midpoint formula between (1, 4) and (x, 10) is (–4, 7), what is the value of x?

solution:

1+x=-8 (or)(1+x/2)=-4
which gives the value x=-9

Study midpoint formula Example 5:

Find the mid point formula of a segment if A is (6,8) and B is (-2, 4).

Solution :

Let (6, 8) be (x1, y1) and    (-2, 4) be (x2, y2).

Therefore their mid point M is given as :

M=[(x1+x2)/2,(y1+y2)/2]

=((6-2)/ 2,(8+4)/2)

= (4/2,12/2)

=(2,6)

Example 6:

If the mid point of segment. AB is (-2, 8) and A is (12, -1), find co-ordinates of B.

Solution :

Let the co-ordinates of B be (x, y). According to the mid-point formula

(-2,8)=[(12+x/2,-1+y/2)]

-2=(12+x)/2, 8=(-1+y)/2

-4=12+x, 16=-1+y

(x,y)=(-16,17)

Therefore the co-ordinates of B are (-16, 17).