A line segment has the endpoints U(1,2) and V(5,0) find the coordinates of its midpoint M

Question

Write the coordinates as decimals or integers
M(__,__)

Answer 1

To find the midpoint \( M \) of a line segment with endpoints \( U(x_1, y_1) \) and \( V(x_2, y_2) \), we use the midpoint formula:

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

Given the endpoints \( U(1, 2) \) and \( V(5, 0) \):

• \( x_1 = 1 \)
• \( y_1 = 2 \)
• \( x_2 = 5 \)
• \( y_2 = 0 \)

Now, we can calculate the coordinates of the midpoint:

\[ M\left( \frac{1 + 5}{2}, \frac{2 + 0}{2} \right) = M\left( \frac{6}{2}, \frac{2}{2} \right) = M(3, 1) \]

So, the coordinates of the midpoint \( M \) are:

\[ M(3, 1) \]