Question

the midpoint of ab is m(1,0). if the coordinates of a are (6,7), 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 $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Given $A(6,7)$ and $M(1,0)$. Let the coordinates of $B$ be $(x,y)$.

Step2: Solve for x - coordinate of B

We have $\frac{6 + x}{2}=1$. Cross - multiply: $6 + x=2$. Then $x=2 - 6=-4$.

Step3: Solve for y - coordinate of B

We have $\frac{7 + y}{2}=0$. Cross - multiply: $7 + y = 0$. Then $y=-7$.

Answer:

$(-4,-7)$