Find the midpoint of the segment with the following endpoints. (7, 5) and (0, 10)
Check the final answer first, then review the worked steps.
Problem
Find the midpoint of the segment with the following endpoints. (7, 5) and (0, 10)
Step-by-step solution
- Identify the Midpoint Formula: The midpoint of a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is found using the formula: $$M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$$ 2. Assign Coordinates: Let the first endpoint be $(x_1, y_1) = (7, 5)$ and the second endpoint be $(x_2, y_2) = (0, 10)$. 3. Calculate the x-coordinate of the midpoint: Substitute the x-values into the formula: $$\frac{x_1 + x_2}{2} = \frac{7 + 0}{2} = \frac{7}{2}$$ 4. Calculate the y-coordinate of the midpoint: Substitute the y-values into the formula: $$\frac{y_1 + y_2}{2} = \frac{5 + 10}{2} = \frac{15}{2}$$ 5. State the Midpoint: Combine the calculated coordinates to find the midpoint. The midpoint is $$\left(\frac{7}{2}, \frac{15}{2}\right)$$.
Answer
$\left(\frac{7}{2}, \frac{15}{2}\right)$