Question

the midpoint of $overline{ab}$ is $m = (-2,1)$. one endpoint is $a = (-5,-4)$. find the coordinates of the other endpoint, $b$.

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 $x_1=-5,y_1 = - 4$, and $M(-2,1)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=-2$. Substitute $x_1=-5$ into the equation: $\frac{-5 + x_2}{2}=-2$. Multiply both sides by 2: $-5+x_2=-4$. Then add 5 to both sides: $x_2=-4 + 5=1$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=1$. Substitute $y_1=-4$ into the equation: $\frac{-4 + y_2}{2}=1$. Multiply both sides by 2: $-4+y_2=2$. Then add 4 to both sides: $y_2=2 + 4=6$.

Answer:

$(1,6)$