Question

question
the midpoint of $overline{ab}$ is $m(-1, -5)$. if the coordinates of $a$ are $(2, -4)$, what are the coordinates of $b$?
answer attempt 1 out of 2

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 $x_1 = 2,y_1=-4,M_x=-1,M_y = - 5$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=M_x$. Substituting the values, we get $\frac{2 + x_2}{2}=-1$. Cross - multiply: $2 + x_2=-2$. Then $x_2=-2 - 2=-4$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=M_y$. Substituting the values, we get $\frac{-4 + y_2}{2}=-5$. Cross - multiply: $-4 + y_2=-10$. Then $y_2=-10 + 4=-6$.

Answer:

$(-4,-6)$