Question

find the length of \\(\overline{st}\\) with coordinates s(-5,-2) and t(-3,4). round your answer to the nearest tenth.
st=

Explanation:

Step1: Recall distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(S(-5,-2)\) so \(x_1=-5,y_1 = - 2\) and \(T(-3,4)\) so \(x_2=-3,y_2 = 4\).

Step2: Calculate differences in coordinates

First, find \(x_2 - x_1=-3-(-5)=-3 + 5 = 2\). Then, find \(y_2 - y_1=4-(-2)=4 + 2 = 6\).

Step3: Substitute into distance formula

Substitute these values into the formula: \(ST=\sqrt{(2)^2+(6)^2}=\sqrt{4 + 36}=\sqrt{40}\).

Step4: Simplify and round

Simplify \(\sqrt{40}\approx6.3\) (rounded to the nearest tenth).

Answer:

\(6.3\)