Question

find endpoint from midpoint and endpoint question the midpoint of $overline{ab}$ is $m(6, - 3)$. if the coordinates of $a$ are $(7, - 4)$, 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 $(x_1,y_1)$ and $(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $A(x_1,y_1)=(7,-4)$ and $B(x_2,y_2)$, and $M(6,-3)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=6$. Substitute $x_1 = 7$ into the equation: $\frac{7+x_2}{2}=6$. Multiply both sides by 2: $7 + x_2=12$. Then subtract 7 from both sides: $x_2=12 - 7=5$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=-3$. Substitute $y_1=-4$ into the equation: $\frac{-4 + y_2}{2}=-3$. Multiply both sides by 2: $-4 + y_2=-6$. Then add 4 to both sides: $y_2=-6 + 4=-2$.

Answer:

$(5,-2)$