Find the coordinates of D if E(-6,4) is the midpoint of DF and F has coordinates (-5,-3)

To find the coordinates of point \( D \), we use the midpoint formula. The midpoint \( E \) of a line segment \( DF \) with endpoints \( D(x_1, y_1) \) and \( F(x_2, y_2) \) is given by:

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

Given:
- Coordinates of \( E = (-6, 4) \)
- Coordinates of \( F = (-5, -3) \)

Let the coordinates of \( D \) be \( (x_1, y_1) \).

According to the midpoint formula:
\[
\frac{x_1 + (-5)}{2} = -6
\]
\[
\frac{y_1 + (-3)}{2} = 4
\]

We can solve these two equations to find \( x_1 \) and \( y_1 \).

1. Solve for \( x_1 \):
\[
\frac{x_1 - 5}{2} = -6
\]
\[
x_1 - 5 = -12 \quad (\text{Multiplying both sides by 2})
\]
\[
x_1 = -7
\]

2. Solve for \( y_1 \):
\[
\frac{y_1 - 3}{2} = 4
\]
\[
y_1 - 3 = 8 \quad (\text{Multiplying both sides by 2})
\]
\[
y_1 = 11
\]

Thus, the coordinates of \( D \) are \( (-7, 11) \).

Would you like more details or have any questions?

Here are some related questions:

1. How do you find the distance between two points?
2. What is the slope of the line passing through points \( D \) and \( F \)?
3. How do you find the equation of a line given two points?
4. How do you verify if a point lies on a given line segment?
5. Can the midpoint formula be extended to three-dimensional space?

**Tip:** When solving problems with the midpoint formula, always double-check by plugging the coordinates back into the formula to ensure accuracy.

Learn how to find the coordinates of point D when E(-6, 4) is the midpoint of segment DF, and F has coordinates (-5, -3). Detailed step-by-step solution using the midpoint formula. Suitable for students in Grades 9-12.

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