Question

el punto medio de $overline{ab}$ es $m = (-1,2)$. uno de los puntos extremos es $a=(-4, - 4)$. hallar las coordenadas del otro punto extremo, $b$.

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $A(x_1,y_1)$ and $B(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $A(-4,-4)$ and $M(-1,2)$. Let $B=(x,y)$.

Step2: Solve for x - coordinate

We have $\frac{-4 + x}{2}=-1$. Multiply both sides by 2: $-4 + x=-2$. Then add 4 to both sides: $x=-2 + 4=2$.

Step3: Solve for y - coordinate

We have $\frac{-4 + y}{2}=2$. Multiply both sides by 2: $-4 + y = 4$. Then add 4 to both sides: $y=4 + 4=8$.

Answer:

$(2,8)$