Question

the midpoint of ab is m(-1,2). if the coordinates of a are (4,5), what are the coordinates of b?

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 $A(x_1,y_1)=(4,5)$ and $B(x_2,y_2)$. The mid - point $M(-1,2)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=-1$. Substitute $x_1 = 4$ into the equation: $\frac{4 + x_2}{2}=-1$. Multiply both sides by 2: $4+x_2=-2$. Then subtract 4 from both sides: $x_2=-2 - 4=-6$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=2$. Substitute $y_1 = 5$ into the equation: $\frac{5 + y_2}{2}=2$. Multiply both sides by 2: $5+y_2 = 4$. Then subtract 5 from both sides: $y_2=4 - 5=-1$.

Answer:

$(-6,-1)$