The problem in the image asks:

"Find the coordinates of the midpoint of the line segment joining the points (7, -3) and (7, -4)."

Solution:

The midpoint $M(x, y)$ of a line segment joining two points $(x_1, y_1)$ and $(x_2, y_2)$ is calculated using the formula: $M\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$

For the given points:

• $(x_1, y_1) = (7, -3)$
• $(x_2, y_2) = (7, -4)$

Plugging the coordinates into the midpoint formula: $M\left( \frac{7 + 7}{2}, \frac{-3 + (-4)}{2} \right)$

Simplifying further: $M\left( \frac{14}{2}, \frac{-7}{2} \right)$ $M(7, -3.5)$

So, the coordinates of the midpoint are $\boxed{(7, -3.5)}$.

Would you like further details or have any other questions?

Follow-up Questions:

1. What is the distance between the points $(7, -3)$ and $(7, -4)$?
2. How do you find the slope of the line segment joining these two points?
3. What are the coordinates of the midpoint if the points were $(7, -3)$ and $(7, 1)$?
4. Can you determine the equation of the line passing through these points?
5. How would the midpoint formula change if the points were in three-dimensional space?

Tip: The midpoint formula can be extended to three dimensions by adding the $z$-coordinates and dividing by 2 as well!