Question

point $m$ is the midpoint of point $a$ and point $b$. find the coordinates of point $b$.
$a(8, 12)$
$m(4, 19)$

Explanation:

Step1: Recall midpoint formula

The midpoint $M(x_m, y_m)$ of $A(x_a, y_a)$ and $B(x_b, y_b)$ is:
$$x_m = \frac{x_a + x_b}{2}, \quad y_m = \frac{y_a + y_b}{2}$$

Step2: Solve for $x_b$

Rearrange x-coordinate formula:
$x_b = 2x_m - x_a$
Substitute $x_m=4, x_a=8$:
$x_b = 2(4) - 8 = 8 - 8 = 0$

Step3: Solve for $y_b$

Rearrange y-coordinate formula:
$y_b = 2y_m - y_a$
Substitute $y_m=19, y_a=12$:
$y_b = 2(19) - 12 = 38 - 12 = 26$

Answer:

$(0, 26)$