Question

place the coordinates that best complete the sentence. the midpoint of line segment ab is point m which is located at (-18,10). point a is located at (3, - 3). the coordinates of point b are

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 $A=(x_1,y_1)=(3,-3)$ and $B=(x_2,y_2)$ and $M=(-18,10)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=x_M$. Substituting $x_1 = 3$ and $x_M=-18$, we get $\frac{3 + x_2}{2}=-18$. Multiply both sides by 2: $3 + x_2=-36$. Then subtract 3 from both sides: $x_2=-36 - 3=-39$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=y_M$. Substituting $y_1=-3$ and $y_M = 10$, we get $\frac{-3 + y_2}{2}=10$. Multiply both sides by 2: $-3 + y_2 = 20$. Then add 3 to both sides: $y_2=20 + 3=23$.

Answer:

$(-39,23)$