solve for each problem and round the answer to the nearest 10th find the length og MR if R is the midpoint of JL J.(-5,7) K.(1,7) M.(-6,4 L.(0,4) R?

To find the length of \( MR \), where \( R \) is the midpoint of \( JL \), we first need to determine the coordinates of \( R \).

1. **Find the coordinates of \( R \)** (midpoint of \( J \) and \( L \)):
   - Coordinates of \( J \): \( (-5, 7) \)
   - Coordinates of \( L \): \( (0, 4) \)

   The midpoint formula is:
   \[
   R\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)
   \]

   Applying the formula:
   \[
   R\left(\frac{-5 + 0}{2}, \frac{7 + 4}{2}\right) = R\left(-2.5, 5.5\right)
   \]

2. **Find the distance \( MR \)** using the distance formula:
   - Coordinates of \( M \): \( (-6, 4) \)
   - Coordinates of \( R \): \( (-2.5, 5.5) \)

   The distance formula is:
   \[
   d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
   \]

   Applying the formula:
   \[
   d = \sqrt{((-2.5) - (-6))^2 + (5.5 - 4)^2}
   \]
   \[
   = \sqrt{(3.5)^2 + (1.5)^2}
   \]
   \[
   = \sqrt{12.25 + 2.25} = \sqrt{14.5}
   \]
   \[
   \approx 3.8
   \]

Thus, the length of \( MR \) is approximately **3.8** when rounded to the nearest tenth.

Would you like details on any specific steps, or do you have any questions? Here are some related questions for further exploration:

1. What other methods can be used to find midpoints?
2. How would the distance change if point \( M \) was moved to a different location?
3. Can you calculate the length of other segments using similar methods?
4. What is the significance of midpoints in geometry?
5. How does the distance formula relate to the Pythagorean theorem?

**Tip:** When calculating midpoints and distances, always check your arithmetic carefully to avoid small mistakes.

Solve for each problem and round the answer to the nearest 10th find the length of MR if R is the midpoint of JL J.(-5,7) K.(1,7) M.(-6,4) L.(0,4) R?

Discover how to calculate the length of segment MR, where R is the midpoint of segment JL, with coordinates J(-5, 7), K(1, 7), M(-6, 4), and L(0, 4). This step-by-step guide utilizes the midpoint and distance formulas, perfect for students in Grades 7-9.

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