QR has a midpoint at M(–17.5, –1). Point R is at (–18, –10). Find the coordinates of point Q.

Write the coordinates as decimals or integers

To find the coordinates of point \( Q(x_1, y_1) \), we can use the midpoint formula. The midpoint \( M \) of a line segment with endpoints \( Q(x_1, y_1) \) and \( R(x_2, y_2) \) is given by:

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

Given:
- Midpoint \( M = (-17.5, -1) \)
- Point \( R = (-18, -10) \)

We need to find \( Q(x_1, y_1) \).

Using the midpoint formula:

\[
-17.5 = \frac{x_1 + (-18)}{2}
\]
\[
-1 = \frac{y_1 + (-10)}{2}
\]

### Solving for \( x_1 \):
\[
-17.5 = \frac{x_1 - 18}{2}
\]
Multiply both sides by 2:
\[
-35 = x_1 - 18
\]
Add 18 to both sides:
\[
x_1 = -35 + 18 = -17
\]

### Solving for \( y_1 \):
\[
-1 = \frac{y_1 - 10}{2}
\]
Multiply both sides by 2:
\[
-2 = y_1 - 10
\]
Add 10 to both sides:
\[
y_1 = -2 + 10 = 8
\]

So, the coordinates of point \( Q \) are \( \boxed{(-17, 8)} \).

Would you like more details or have any questions?  
Here are five related questions to consider:

1. How do you find the distance between two points?
2. What is the formula for finding the slope of a line segment?
3. How do you find the equation of a line given two points?
4. What are the coordinates of a point if the midpoint and one endpoint are given as variables?
5. How can you verify if a given point lies on a line segment?

**Tip:** Always verify your calculations by substituting back into the original formula.

Learn how to find the coordinates of point Q given the midpoint (-17.5, -1) and endpoint R (-18, -10). This problem involves applying the midpoint formula in coordinate geometry. 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