Question

What is midpoint formula class 10?

Answer 1

The midpoint formula is used to find the exact middle point between two given points in a coordinate plane. It is helpful in geometry and coordinate geometry to determine the center point of a line segment.

The formula for the midpoint \( M \) of a line segment joining two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is:

\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]

Steps to use the midpoint formula:

1. Identify the coordinates of the two points: \( A(x_1, y_1) \) and \( B(x_2, y_2) \).
   

1. Add the x-coordinates together and divide by 2 to get the x-coordinate of the midpoint.
   

1. Add the y-coordinates together and divide by 2 to get the y-coordinate of the midpoint.
   

Example:

If you have the points \( A(1, 2) \) and \( B(3, 4) \), the midpoint is:

\[
M = \left( \frac{1 + 3}{2}, \frac{2 + 4}{2} \right) = \left( \frac{4}{2}, \frac{6}{2} \right) = (2, 3)
\]

So, the midpoint of \( A(1, 2) \) and \( B(3, 4) \) is \( M(2, 3) \).