Question

if \\( \overline { t v } \\) has endpoints at \\( t ( 3,9 ) \\) and \\( v ( - 3, - 5 ) \\), what is the length of \\( \overline { t v } \\)?
round your answer to the nearest hundredth.
use the keypad to enter the answer in the box provided.
the length of \\( \overline { t v } \\) is \\( \square \\) units.

Explanation:

Step1: Identify the coordinates

Let \(T(x_1,y_1)=(3,9)\) and \(V(x_2,y_2)=(-3,-5)\)

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values: \(x_2 - x_1=-3 - 3=-6\), \(y_2 - y_1=-5 - 9=-14\)
So \(d=\sqrt{(-6)^2+(-14)^2}=\sqrt{36 + 196}=\sqrt{232}\)

Step3: Calculate the square - root

\(\sqrt{232}\approx15.23\)

Answer:

\(15.23\)