Question

el punto medio de $overline{st}$ es $m = (-1, -2)$. uno de los puntos extremos es $s=(3,2)$. hallar las coordenadas del otro punto extremo, $t$.

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $S=(x_1,y_1)=(3,2)$ and $T=(x_2,y_2)$, and $M=(-1,-2)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=-1$. Substitute $x_1 = 3$ into the equation: $\frac{3 + x_2}{2}=-1$. Multiply both sides by 2: $3+x_2=-2$. Then subtract 3 from both sides: $x_2=-2 - 3=-5$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=-2$. Substitute $y_1 = 2$ into the equation: $\frac{2 + y_2}{2}=-2$. Multiply both sides by 2: $2+y_2=-4$. Then subtract 2 from both sides: $y_2=-4 - 2=-6$.

Answer:

$(-5,-6)$