Question

The points R(3,−3), S(8,0), and T(4,1) are connected to form △RST.

What is the most appropriate classification of △RST?

right isosceles
isosceles
scalene
equilateral

Answer 1

right isosceles

rs:34&rs=rt+st

rt:17

st:17

ab=[(x(a)-x(b))+(y(a)+y(b))]

Answer 2

Isosceles.

Explanation:

We are going to check it with the distance formula

d(R,T) =
`\sqrt[2]{(3-4)^(2)+(-3-1)^(2)}`

=
`\sqrt[2]{(-1)^(2)+(-4)^(2)}`

=
`\sqrt[2]{1+16}`

=
`\sqrt[2]{17}`.

d(T,S) =
`\sqrt[2]{(4-8)^(2)+(1-0)^(2)}`

=
`\sqrt[2]{(-4)^(2)+(1)^(2)}`

=
`\sqrt[2]{16+1}`

=
`\sqrt[2]{17}`.

d(S,R) =
`\sqrt[2]{(8-3)^(2)+(0-(-3))^(2)}`

=
`\sqrt[2]{(5)^(2)+(3)^(2)}`

=
`\sqrt[2]{25+9}`

=
`\sqrt[2]{34}`.

Then, as the triangle has two sides with the same length, the triangle is isosceles.