Question

1. use the distance formula to find the lengths of the sides of the second triangle, (\triangle stu).

(su=sqrt{(-2-(-8))^{2}+(-7-(-3))^{2}}=sqrt{6^{2}+(-4)^{2}})
(=sqrt{36 + 16}=sqrt{52}=sqrt{4(13)}=2sqrt{13})
the length of (overline{st}) is 5. what is the length of (overline{tu})?
(sqrt{53})
(sqrt{85})
(sqrt{45})

Explanation:

Step1: Identify coordinates

The coordinates of \(T(-4,0)\) and \(U(-2,-7)\)

Step2: Apply distance formula

The distance formula is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here \(x_1=-4,y_1 = 0,x_2=-2,y_2=-7\)

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Answer:

\(\sqrt{53}\)