Question

question the midpoint of $overline{ab}$ is $m(6,2)$. 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 $A(x_1,y_1)$ and $B(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $A(7,-4)$ and $M(6,2)$.

Step2: Find the x - coordinate of B

We know that $\frac{x_1 + x_2}{2}=x_M$. Substituting $x_1 = 7$ and $x_M=6$, we get $\frac{7 + x_2}{2}=6$. Cross - multiply: $7 + x_2=12$. Then $x_2=12 - 7=5$.

Step3: Find the y - coordinate of B

We know that $\frac{y_1 + y_2}{2}=y_M$. Substituting $y_1=-4$ and $y_M = 2$, we get $\frac{-4 + y_2}{2}=2$. Cross - multiply: $-4 + y_2 = 4$. Then $y_2=4 + 4=8$.

Answer:

$(5,8)$