Question

find the coordinates of the midpoint of a segment with the given endpoints. 5. t(3, 1), u(5, 3) 6. j(-4, 2), t(5, -2)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: For points $T(3,1)$ and $U(5,3)$

Calculate the x - coordinate of the mid - point: $\frac{3 + 5}{2}=\frac{8}{2}=4$. Calculate the y - coordinate of the mid - point: $\frac{1+3}{2}=\frac{4}{2}=2$. So the mid - point of segment $TU$ is $(4,2)$.

Step3: For points $J(-4,2)$ and $T(5,-2)$

Calculate the x - coordinate of the mid - point: $\frac{-4 + 5}{2}=\frac{1}{2}=0.5$. Calculate the y - coordinate of the mid - point: $\frac{2+( - 2)}{2}=\frac{0}{2}=0$. So the mid - point of segment $JT$ is $(0.5,0)$.

Answer:

The mid - point of segment with endpoints $T(3,1)$ and $U(5,3)$ is $(4,2)$.
The mid - point of segment with endpoints $J(-4,2)$ and $T(5,-2)$ is $(0.5,0)$.