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.