what is the midpoint of the segment shown below
What is the midpoint of the segment shown below?
Answer:
To find the midpoint of a line segment, you can use the midpoint formula. Assuming you have the coordinates of the endpoints of the segment, let’s denote these points as ( (x_1, y_1) ) and ( (x_2, y_2) ).
The formula to find the midpoint ( M ) of a segment with these endpoints is given by:
M \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
Example:
Let’s say the endpoints of the segment are ( (2, 3) ) and ( (6, 7) ). Using the midpoint formula, we can calculate the midpoint as follows:
M \left( \frac{2 + 6}{2}, \frac{3 + 7}{2} \right)
- Calculate the average of the ( x )-coordinates:
\frac{2 + 6}{2} = \frac{8}{2} = 4
- Calculate the average of the ( y )-coordinates:
\frac{3 + 7}{2} = \frac{10}{2} = 5
So, the midpoint ( M ) of the segment is ( (4, 5) ).
If you have the coordinates for different endpoints, just plug them into the formula. The process will always involve averaging the ( x )-coordinates and the ( y )-coordinates of the endpoints to find the midpoint.