Find the missing endpoint T on RT  with midpoint S if  point R is ( -9, 8 ) and point S is (2, -5)

 

To find the missing endpoint \( T(x, y) \) on segment \( RT \), given the midpoint \( S(2, -5) \) and endpoint \( R(-9, 8) \), we can use the midpoint formula.

The midpoint formula is:

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

Given:
- \( R(x_1, y_1) = (-9, 8) \)
- \( S(x_m, y_m) = (2, -5) \)
- \( T(x_2, y_2) = (x, y) \) (which we need to find)

Using the midpoint formula, we can set up the following equations for the \( x \) and \( y \) coordinates:

\[
\frac{-9 + x}{2} = 2
\]

\[
\frac{8 + y}{2} = -5
\]

### Solve for \( x \):

\[
\frac{-9 + x}{2} = 2
\]

Multiply both sides by 2:

\[
-9 + x = 4
\]

Add 9 to both sides:

\[
x = 13
\]

### Solve for \( y \):

\[
\frac{8 + y}{2} = -5
\]

Multiply both sides by 2:

\[
8 + y = -10
\]

Subtract 8 from both sides:

\[
y = -18
\]

### Conclusion:

The missing endpoint \( T \) is \( (13, -18) \).

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

Here are some related questions to explore further:

1. How do you find the midpoint if you are given both endpoints?
2. What is the distance formula between two points in a coordinate plane?
3. How can the midpoint formula be applied in three-dimensional space?
4. Can you determine the slope of the line segment \( RT \) given points \( R \) and \( T \)?
5. How does the concept of vectors relate to finding midpoints and endpoints?

**Tip:** Always double-check your calculations when solving for unknowns to avoid simple errors, especially with signs (positive or negative).

Find the missing endpoint T on RT with midpoint S if point R is (-9, 8) and point S is (2, -5)

Discover how to find the missing endpoint T on a line segment RT, with given point R (-9, 8) and midpoint S (2, -5). This problem explores the application of the midpoint formula in coordinate geometry and algebra, suitable for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation