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.
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
$\left(\frac{7}{2}, \frac{15}{2}\right)$