Question

question
the mid - point of ab is m(3,2). if the coordinates of a are (1,7), what are the coordinates of b?
the mid - point of ab is m(3,2). if the coordinates of a are (1,7), 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 $A(1,7)$ and $M(3,2)$, where $x_1 = 1,y_1 = 7,\frac{x_1 + x_2}{2}=3,\frac{y_1 + y_2}{2}=2$.

Step2: Solve for $x_2$

We have $\frac{x_1 + x_2}{2}=3$. Substitute $x_1 = 1$ into the equation: $\frac{1 + x_2}{2}=3$. Multiply both sides by 2: $1+x_2 = 6$. Then subtract 1 from both sides: $x_2=6 - 1=5$.

Step3: Solve for $y_2$

We have $\frac{y_1 + y_2}{2}=2$. Substitute $y_1 = 7$ into the equation: $\frac{7 + y_2}{2}=2$. Multiply both sides by 2: $7 + y_2=4$. Then subtract 7 from both sides: $y_2=4 - 7=-3$.

Answer:

$(5,-3)$