The document discusses how to calculate the length of a line segment and the coordinates of the midpoint of a line segment given two points on the line. To calculate the length, the formula is: Length = √(x2 - x1)2 + (y2 - y1)2, where (x2, y2) are the coordinates of one endpoint and (x1, y1) are the coordinates of the other endpoint. To calculate the midpoint, the formula is: Midpoint = (x2+x1/2, y2+y1/2). An example of calculating both the length and midpoint of the line segment between points (-3,4) and (2

1. 7.11 – DETERMINE FROM THE COORDINATES ON A LINE SEGMENT THE LENGTH OF THE
LINE AND THE COORDINATES OF THE MIDPOINT
OBJETIVE: At the end of this lesson you will be able to determine the coordinates on a line
segment the length of a line and the coordinates of the midpoint of the line.
We will approach this lesson in two parts:
1) Length of a Line
To calculate the length of a line, we use the following formula:
Length of line AB = √(𝒙 𝟐 − 𝒙 𝟏) 𝟐 + (𝒚 𝟐 − 𝒚 𝟏) 𝟐
where x2 and y2 are coordinates on the line furthest to the right
x1 and y1 are coordinates on the line furthest to the left
Now, we will look at how to use this formula:
Example 1:
Q: Calculate the length of the line AB below:
1st
: Identify x2, y2, x1, y1.
We know that x2 and y2 are the coordinates on the
right-hand side of the graph. This point is (2, -3).
This means that x1 and y1 is (-3, 4).
2nd : Substitute the values into the formula
We simply replace x2, y2, x1 and y1 with their values in
the formula:
Length of line AB = √(𝑥2 − 𝑥1)2 + (𝑦2 − 𝑦1)2
= √(2 − (−3))2 + (−3 − 4)2
= √(5)2 + (−7)2
= √25 + 49
= √74

2. 7.11 – DETERMINE FROM THE COORDINATES ON A LINE SEGMENT THE LENGTH OF THE
LINE AND THE COORDINATES OF THE MIDPOINT
= 8.6 units
So, the length of the line AB is approximately 8.6 units.
Watch this video to get another example:
https://www.youtube.com/watch?v=UpI11modN68
Simple right? Now let us move on.
2) Midpoint of a Line
To find the midpoint of a line we use a formula:
Midpoint of Line AB = (
𝒙 𝟐+𝒙 𝟏
𝟐
,
𝒚 𝟐+𝒚 𝟏
𝟐
)
Notice that this formula gives us the
COORDINATE for the midpoint.
The steps are the same as finding the length of the
line:
1) Find x2, y2, x1 and y1.
2) Substitute values into the equation and calculate.
Have a look at this video which shows us how to do this:
https://www.youtube.com/watch?v=Zgx56llSHVE
Midpoint – punto medio

3. 7.11 – DETERMINE FROM THE COORDINATES ON A LINE SEGMENT THE LENGTH OF THE
LINE AND THE COORDINATES OF THE MIDPOINT