Question

1. m is the midpoint of ab. if the coordinates of a are (-1,5) and the coordinates of m are (3,-8), what are the coordinates of 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 $x_1=-1,y_1 = 5$ and the mid - point $M$ has coordinates $(3,-8)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=3$. Substitute $x_1=-1$ into the equation: $\frac{-1 + x_2}{2}=3$. Multiply both sides by 2: $-1+x_2 = 6$. Then add 1 to both sides: $x_2=7$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=-8$. Substitute $y_1 = 5$ into the equation: $\frac{5 + y_2}{2}=-8$. Multiply both sides by 2: $5 + y_2=-16$. Then subtract 5 from both sides: $y_2=-21$.

Answer:

$(7,-21)$