The endpoints of YZ​ are Y(1, −6)​ and Z(−2, 8)​ . Find the coordinates of the midpoint M​ . 

Midpoint: M​ (, )

Find YZ​ . Round your answer to the nearest tenth if necessary. 

YZ=​  


To find the midpoint \( M \) of a line segment, we use the midpoint formula:

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

Given the endpoints \( Y(1, -6) \) and \( Z(-2, 8) \), we can plug the coordinates into the formula.

### Step 1: Calculate the midpoint
\[
M = \left( \frac{1 + (-2)}{2}, \frac{-6 + 8}{2} \right)
\]
\[
M = \left( \frac{1 - 2}{2}, \frac{-6 + 8}{2} \right)
\]
\[
M = \left( \frac{-1}{2}, \frac{2}{2} \right)
\]
\[
M = \left( -0.5, 1 \right)
\]

Thus, the midpoint \( M \) is \( (-0.5, 1) \).

### Step 2: Find the distance \( YZ \)
The distance formula between two points is:

\[
YZ = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Substituting the coordinates of \( Y(1, -6) \) and \( Z(-2, 8) \):

\[
YZ = \sqrt{(-2 - 1)^2 + (8 - (-6))^2}
\]
\[
YZ = \sqrt{(-3)^2 + (14)^2}
\]
\[
YZ = \sqrt{9 + 196}
\]
\[
YZ = \sqrt{205}
\]
\[
YZ \approx 14.3
\]

Thus, the distance \( YZ \) is approximately 14.3 units.

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Would you like more details on the steps, or do you have any questions?

Here are 5 related questions to further explore:
1. How would the midpoint change if the coordinates of \( Y \) and \( Z \) were reversed?
2. Can you find the slope of the line passing through points \( Y \) and \( Z \)?
3. How would the distance change if the points were closer together?
4. How is the distance formula related to the Pythagorean theorem?
5. Can you find the equation of the line that passes through points \( Y \) and \( Z \)?

**Tip:** The midpoint formula finds the average of the x- and y-coordinates, making it an easy way to split a segment exactly in half.

The endpoints of YZ are Y(1, −6) and Z(−2, 8). Find the coordinates of the midpoint M. Midpoint: M (, ). Find YZ. Round your answer to the nearest tenth if necessary. YZ =

Learn how to find the midpoint and distance between the points Y(1, -6) and Z(-2, 8) using the midpoint and distance formulas. This step-by-step guide covers key concepts in geometry and coordinate geometry, suitable for students in Grades 8-10.

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