5. A and B are the mid-points of the two given numbers. What numbers will you
put in place of A and B?
A
1000
2000
500
750
Answers
Explanation:
The midpoint
m
of two numbers
a
and
b
is, by definition, a number that is the same distance from
a
as it is from
b
.
Using this, we can get a formula for the midpoint
m
in terms of
a
and
b
.
Picture
a
and
b
as two points on a number line, with
a
to the left of
b
. Now,
m
must be between them, so
m
is greater than
a
but less than
b
. So if the distance from
a
to
m
is the same as the distance from
m
to
b
, we can set these two distances to be equal, like this:
m
−
a
=
b
−
m
This equation says: "The difference between
m
and
a
is the same as the difference between
b
and
m
."
Now, all we do is rearrange this to equation to solve for
m
:
m
−
a
+
m
=
b
(add
m
to both sides)
2
m
=
b
+
a
(add
a
to both sides)
m
=
b
+
a
2
(divide both sides by 2)
And there it is—the formula for the midpoint! This is often called the average of the two numbers
a
and
b
, and written as
m
=
a
+
b
2