Question

a line segment has a midpoint of (3, 1/2). if one endpoint is (5,4), what is the other endpoint? the other endpoint is (type an ordered pair. simplify your answer)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let the mid - point $M=(3,\frac{1}{2})$ and one endpoint $A=(5,4)$, and the other endpoint be $B=(x,y)$.

Step2: Solve for x - coordinate

We know that $\frac{5 + x}{2}=3$. Cross - multiply: $5 + x=6$. Then $x=6 - 5=1$.

Step3: Solve for y - coordinate

We know that $\frac{4 + y}{2}=\frac{1}{2}$. Cross - multiply: $4 + y = 1$. Then $y=1 - 4=-3$.

Answer:

$(1,-3)$