Find the midpoint of the segment with the following endpoints. (6, 7) and (-1, -1)

Check the final answer first, then review the worked steps.

Problem

Find the midpoint of the segment with the following endpoints. (6, 7) and (-1, -1)

Answer

[2.5, 3]

Step-by-step solution

1. Identify the Midpoint Formula: The midpoint formula is used to find the coordinates of the midpoint of a line segment given its two endpoints. If the endpoints are $(x_1, y_1)$ and $(x_2, y_2)$, the midpoint $(x_m, y_m)$ is given by:
$$x_m = \frac{x_1 + x_2}{2}$$ $$y_m = \frac{y_1 + y_2}{2}$$
2. Identify the Given Endpoints: The problem provides two endpoints for the line segment: $(6, 7)$ and $(-1, -1)$. We can assign these values as follows:
$x_1 = 6$
$y_1 = 7$
$x_2 = -1$
$y_2 = -1$
3. Calculate the x-coordinate of the Midpoint: Substitute the x-values of the endpoints into the midpoint formula for the x-coordinate:
$$x_m = \frac{6 + (-1)}{2}$$ $$x_m = \frac{6 - 1}{2}$$ $$x_m = \frac{5}{2}$$ $$x_m = 2.5$$
4. Calculate the y-coordinate of the Midpoint: Substitute the y-values of the endpoints into the midpoint formula for the y-coordinate:
$$y_m = \frac{7 + (-1)}{2}$$ $$y_m = \frac{7 - 1}{2}$$ $$y_m = \frac{6}{2}$$ $$y_m = 3$
5. State the Midpoint Coordinates: Combine the calculated x and y coordinates to form the midpoint of the segment.
The midpoint is $(2.5, 3)$.