A line segment has the endpoints S(9, 5) and T(7, 9). Find the coordinates of its midpoint M.

To find the coordinates of the midpoint \( M \) of a line segment with endpoints \( S(x_1, y_1) \) and \( T(x_2, y_2) \), you can use the midpoint formula:

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

Given the endpoints:

- \( S(9, 5) \) where \( x_1 = 9 \) and \( y_1 = 5 \)
- \( T(7, 9) \) where \( x_2 = 7 \) and \( y_2 = 9 \)

Plugging these values into the midpoint formula, we get:

\[
M = \left( \frac{9 + 7}{2}, \frac{5 + 9}{2} \right)
\]

Calculating each component:

\[
M_x = \frac{9 + 7}{2} = \frac{16}{2} = 8
\]

\[
M_y = \frac{5 + 9}{2} = \frac{14}{2} = 7
\]

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

\[
M = (8, 7)
\]

Would you like more details on this calculation or have any questions?

Here are some related questions you might find interesting:

1. How do you find the distance between two points?
2. What is the slope of the line passing through points \( S \) and \( T \)?
3. How would you find the equation of the line segment \( ST \)?
4. How do you find the equation of a perpendicular bisector of a line segment?
5. What is the length of the line segment between points \( S(9, 5) \) and \( T(7, 9) \)?

**Tip:** When calculating the midpoint, averaging the x-coordinates and y-coordinates separately gives the exact center point of the line segment.

Learn how to find the midpoint of a line segment with endpoints S(9, 5) and T(7, 9). Step-by-step calculation using the midpoint formula. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation