Question

question 5 (multiple choice worth 1 points)
(04.01r mc)

δstu is located at s (-3, 0), t (0, -3), and u (3, -3). which statement correctly classifies δstu?

δstu is a scalene triangle.

δstu is an isosceles triangle.

δstu is an equilateral triangle.

δstu is a right triangle

Explanation:

Step1: Calculate the lengths of the sides using the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

For \(ST\):
\(S(-3,0)\) and \(T(0,-3)\)
\(ST=\sqrt{(0 + 3)^2+(-3 - 0)^2}=\sqrt{9 + 9}=\sqrt{18}=3\sqrt{2}\)
For \(TU\):
\(T(0,-3)\) and \(U(3,-3)\)
\(TU=\sqrt{(3 - 0)^2+(-3+ 3)^2}=\sqrt{9+0}=3\)
For \(SU\):
\(S(-3,0)\) and \(U(3,-3)\)
\(SU=\sqrt{(3 + 3)^2+(-3 - 0)^2}=\sqrt{36 + 9}=\sqrt{45}=3\sqrt{5}\)

Step2: Check the properties of the triangle

Since \(ST = 3\sqrt{2}\), \(TU=3\), \(SU = 3\sqrt{5}\), and no two sides are equal (\(3\sqrt{2}
eq3\), \(3\sqrt{2}
eq3\sqrt{5}\), \(3
eq3\sqrt{5}\)), it is not an isosceles or equilateral triangle.
Also, check for right - triangle using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\).
\(ST^{2}=(3\sqrt{2})^{2}=18\), \(TU^{2}=9\), \(SU^{2}=45\)
\(ST^{2}+TU^{2}=18 + 9=27
eq45=SU^{2}\)
\(ST^{2}+SU^{2}=18+45 = 63
eq9=TU^{2}\)
\(TU^{2}+SU^{2}=9 + 45=54
eq18=ST^{2}\)

Answer:

\(\triangle STU\) is a scalene triangle.