Question

the midpoint of $overline{uv}$ is $m(8.05, 6.25)$. one endpoint is $v(4.2, 4.1)$. find the coordinates of the other endpoint $u$.
write the coordinates as decimals or integers.
$u = (\square, \square)$

Explanation:

Step1: Recall midpoint formula

The midpoint $M(x_m, y_m)$ of a segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is given by:
$$x_m = \frac{x_1 + x_2}{2}, \quad y_m = \frac{y_1 + y_2}{2}$$
Let $U=(x, y)$ and $V=(4.2, 4.1)$, $M=(8.05, 6.25)$.

Step2: Solve for x-coordinate of U

Rearrange midpoint formula for $x$:
$$x = 2x_m - x_2$$
Substitute $x_m=8.05$, $x_2=4.2$:
$$x = 2(8.05) - 4.2 = 16.1 - 4.2 = 11.9$$

Step3: Solve for y-coordinate of U

Rearrange midpoint formula for $y$:
$$y = 2y_m - y_2$$
Substitute $y_m=6.25$, $y_2=4.1$:
$$y = 2(6.25) - 4.1 = 12.5 - 4.1 = 8.4$$

Answer:

$U=(11.9, 8.4)$