Question

find the coordinates of the mid - point m of $overline{st}$. then find the distance between points s and t. round the distance to the nearest tenth. s(-2,-4) and t(3,9). the mid - point is m( ). the distance between s and t is about

Explanation:

Step1: Use mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Given $S(-2,-4)$ and $T(3,9)$, we have $x_1=-2,y_1 = - 4,x_2=3,y_2 = 9$. Then $\frac{x_1 + x_2}{2}=\frac{-2 + 3}{2}=\frac{1}{2}=0.5$ and $\frac{y_1 + y_2}{2}=\frac{-4+9}{2}=\frac{5}{2}=2.5$.

Step2: Use distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Substitute $x_1=-2,y_1 = - 4,x_2=3,y_2 = 9$ into the formula: $(x_2 - x_1)^2=(3-(-2))^2=(3 + 2)^2=25$, $(y_2 - y_1)^2=(9-(-4))^2=(9 + 4)^2=169$. Then $d=\sqrt{25 + 169}=\sqrt{194}\approx13.9$.

Answer:

The midpoint is $M(0.5,2.5)$. The distance between $S$ and $T$ is about $13.9$.