If E is the midpoint of DF, find the coordinates of D if E(6, -1) and F(8, -4).

To find the coordinates of point \( D \) given that \( E \) is the midpoint of \( DF \), we can use the midpoint formula. The midpoint formula states that if \( E(x, y) \) is the midpoint of \( D(x_1, y_1) \) and \( F(x_2, y_2) \), then:

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

Given:

- \( E(6, -1) \)
- \( F(8, -4) \)

Let's denote the coordinates of \( D \) as \( (x_1, y_1) \).

Substituting the known values into the midpoint formula:

\[
\left( \frac{x_1 + 8}{2}, \frac{y_1 - 4}{2} \right) = (6, -1)
\]

Now, we can set up equations for each coordinate:

1. For the x-coordinate:
   \[
   \frac{x_1 + 8}{2} = 6
   \]

   Multiply both sides by 2 to solve for \( x_1 \):
   \[
   x_1 + 8 = 12
   \]
   \[
   x_1 = 12 - 8
   \]
   \[
   x_1 = 4
   \]

2. For the y-coordinate:
   \[
   \frac{y_1 - 4}{2} = -1
   \]

   Multiply both sides by 2 to solve for \( y_1 \):
   \[
   y_1 - 4 = -2
   \]
   \[
   y_1 = -2 + 4
   \]
   \[
   y_1 = 2
   \]

So, the coordinates of point \( D \) are \( (4, 2) \).

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

### Related Questions:

1. How do you find the distance between two points in a coordinate plane?
2. What is the formula for the slope of a line passing through two points?
3. How can you find the coordinates of a point dividing a line segment in a given ratio?
4. How do you find the area of a triangle formed by three given points in a plane?
5. What is the equation of a line perpendicular to a given line passing through a specific point?

### Tip:

When using the midpoint formula, always make sure to carefully solve for each coordinate separately to avoid mistakes.

Learn how to find the coordinates of point D when given that E is the midpoint of line segment DF, with E(6, -1) and F(8, -4). This problem involves using the midpoint formula in coordinate geometry. Suitable for Grades 9-10.

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