Question

Find the coordinates of the midpoint MM of ST. Then find the distance between points SS and TT. Round the distance to the nearest tenth. S(−2, 4) and T(3, 9)

Answer 1

The midpoint is $(\frac{1}{2}, \frac{13}{2})$

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:

$m(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$

Here in this sum,

$(x_1, y_1) = (-2, 4)\\\\(x_2, y_2) = (3, 9)$

Substituting the values, we get

$m(x, y)=\left(\frac{-2+3}{2}, \frac{4+9}{2}\right)\\\\m(x, y)=\left(\frac{1}{2}, \frac{13}{2})$

Thus the midpoint is $(\frac{1}{2}, \frac{13}{2})$

Find the distance between points

The distance is given by formula:

$d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$

Here in this sum,

$(x_1, y_1) = (-2, 4)\\\\(x_2, y_2) = (3, 9)$

Substituting the values, we get

$\begin{aligned}&d=\sqrt{(3-(-2))^{2}+(9-4)^{2}}\\\\&d=\sqrt{5^{2}+5^{2}}\\\\&d=\sqrt{25+25}\\\\&d=\sqrt{50}=7.071 \approx 7.1\end{aligned}$

Thus the distance between points S and T is 7.1 units