The midpoint is [tex](\frac{1}{2}, \frac{13}{2})[/tex]
The distance between points S and T is 7.1 units
Solution:
Given points are S(−2, 4) and T(3, 9)
Find the coordinates of the midpoint of ST
The midpoint is given as:
[tex]m(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]
Here in this sum,
[tex](x_1, y_1) = (-2, 4)\\\\(x_2, y_2) = (3, 9)[/tex]
Substituting the values, we get
[tex]m(x, y)=\left(\frac{-2+3}{2}, \frac{4+9}{2}\right)\\\\m(x, y)=\left(\frac{1}{2}, \frac{13}{2})[/tex]
Thus the midpoint is [tex](\frac{1}{2}, \frac{13}{2})[/tex]
Find the distance between points
The distance is given by formula:
[tex]d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}[/tex]
Here in this sum,
[tex](x_1, y_1) = (-2, 4)\\\\(x_2, y_2) = (3, 9)[/tex]
Substituting the values, we get
[tex]\begin{aligned}&d=\sqrt{(3-(-2))^{2}+(9-4)^{2}}\\\\&d=\sqrt{5^{2}+5^{2}}\\\\&d=\sqrt{25+25}\\\\&d=\sqrt{50}=7.071 \approx 7.1\end{aligned}[/tex]
Thus the distance between points S and T is 7.1 units
