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BARSIC [14]
3 years ago
7

Find the coordinates of the midpoint MM of ST. Then find the distance between points SS and TT. Round the distance to the neares

t tenth. S(−2, 4) and T(3, 9)
Mathematics
1 answer:
Andrew [12]3 years ago
7 0

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

The distance between points S and T is 7.1 units

<em><u>Solution:</u></em>

Given points are S(−2, 4) and T(3, 9)

<em><u>Find the coordinates of the midpoint of ST</u></em>

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})

<em><u>Find the distance between points</u></em>

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

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