Question

question the midpoint of ab is m(1,2). if the coordinates of a are (-1,3), 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 $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Given $A(-1,3)$ and $M(1,2)$. Let the coordinates of $B$ be $(x,y)$.

Step2: Solve for $x$ - coordinate of $B$

We have $\frac{-1 + x}{2}=1$. Multiply both sides by 2: $-1 + x = 2$. Then add 1 to both sides: $x=2 + 1=3$.

Step3: Solve for $y$ - coordinate of $B$

We have $\frac{3 + y}{2}=2$. Multiply both sides by 2: $3 + y = 4$. Then subtract 3 from both sides: $y=4 - 3 = 1$.

Answer:

$(3,1)$