Question

the mid - point of ab is m(1,1). if the coordinates of a are (6,8), 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 $x_1 = 6,y_1 = 8$ and $M(1,1)$.

Step2: Solve for $x_2$

We have $\frac{x_1 + x_2}{2}=1$. Substitute $x_1 = 6$ into it: $\frac{6 + x_2}{2}=1$. Cross - multiply gives $6 + x_2=2$. Then $x_2=2 - 6=-4$.

Step3: Solve for $y_2$

We have $\frac{y_1 + y_2}{2}=1$. Substitute $y_1 = 8$ into it: $\frac{8 + y_2}{2}=1$. Cross - multiply gives $8 + y_2=2$. Then $y_2=2 - 8=-6$.

Answer:

$(-4,-6)$