whats the midpoint? Graph the points 

​A(negative 1−1​,negative 2−2​), 

​B(33​,negative 4−4​), 

​C(66​,44​), 

and 

​D(22​,66​). 

Draw 

parallelogramparallelogram 

ABCD and diagonals 

AC overbarAC 

and 

BD overbarBD


### 1. Finding the Midpoint of Diagonals AC and BD

Given the points:
- \( A(-1, -2) \)
- \( B(3, -4) \)
- \( C(6, 4) \)
- \( D(2, 6) \)

We can find the midpoints of diagonals \( AC \) and \( BD \) using the midpoint formula.

#### Midpoint of Diagonal \( AC \):
\[
\text{Midpoint of } AC = \left( \frac{x_A + x_C}{2}, \frac{y_A + y_C}{2} \right)
\]
\[
= \left( \frac{-1 + 6}{2}, \frac{-2 + 4}{2} \right)
= \left( \frac{5}{2}, \frac{2}{2} \right)
= \left( 2.5, 1 \right)
\]

#### Midpoint of Diagonal \( BD \):
\[
\text{Midpoint of } BD = \left( \frac{x_B + x_D}{2}, \frac{y_B + y_D}{2} \right)
\]
\[
= \left( \frac{3 + 2}{2}, \frac{-4 + 6}{2} \right)
= \left( \frac{5}{2}, \frac{2}{2} \right)
= \left( 2.5, 1 \right)
\]

### 2. Graphing the Points and Parallelogram

To graph the parallelogram \( ABCD \) and the diagonals \( AC \) and \( BD \), plot the points \( A(-1, -2) \), \( B(3, -4) \), \( C(6, 4) \), and \( D(2, 6) \). Then, connect the points \( A \) to \( B \), \( B \) to \( C \), \( C \) to \( D \), and \( D \) to \( A \) to form the parallelogram. Finally, draw the diagonals \( AC \) and \( BD \), and note that their midpoints coincide at \( (2.5, 1) \).

Since I can't graph directly, I'll guide you through the plotting process:

1. **Plot Points**:
   - Plot \( A(-1, -2) \)
   - Plot \( B(3, -4) \)
   - Plot \( C(6, 4) \)
   - Plot \( D(2, 6) \)

2. **Draw Parallelogram ABCD**:
   - Draw a line from \( A \) to \( B \)
   - Draw a line from \( B \) to \( C \)
   - Draw a line from \( C \) to \( D \)
   - Draw a line from \( D \) to \( A \)

3. **Draw Diagonals**:
   - Draw diagonal \( AC \) from point \( A(-1, -2) \) to point \( C(6, 4) \).
   - Draw diagonal \( BD \) from point \( B(3, -4) \) to point \( D(2, 6) \).
   - Mark the midpoint \( (2.5, 1) \) on both diagonals.

Would you like further clarification or additional help with another topic?

Here are some follow-up questions:
1. What properties of the parallelogram can be observed from the diagonals' midpoints?
2. How would the midpoint change if one of the points was shifted?
3. Can you derive a formula to find the area of parallelogram \( ABCD \)?
4. What is the slope of each side of parallelogram \( ABCD \)?
5. How do the slopes of the diagonals compare in a parallelogram?

**Tip:** The fact that the diagonals of a parallelogram bisect each other is a key property that can help verify the accuracy of your graph.

Learn how to find the midpoints of diagonals AC and BD in parallelogram ABCD using the midpoint formula. Graph the points A(-1, -2), B(3, -4), C(6, 4), and D(2, 6) to visualize the parallelogram and its diagonals. Understand the properties of parallelogram diagonals. Suitable for high school students.

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