The verticies of triangle RST are R(3, 2), S(-2, 3) and T(-2, 1).

Which describes triangle RST?

1) isosceles

2) scalene

3) equilateral

4) none of the above

1) Isosceles

To determine the type of triangle RST, we need to compare the lengths of its sides.

Using the distance formula, we can find the lengths of each side:

SR = sqrt((-2 - 3)^2 + (3 - 2)^2)
= sqrt((-5)^2 + (1)^2)
= sqrt(25 + 1)
= sqrt(26)

RT = sqrt((-2 - (-2))^2 + (1 - 3)^2)
= sqrt((0)^2 + (-2)^2)
= sqrt(0 + 4)
= sqrt(4)
= 2

TS = sqrt((-2 - 3)^2 + (1 - 2)^2)
= sqrt((-5)^2 + (-1)^2)
= sqrt(25 + 1)
= sqrt(26)

Since all three sides of triangle RST have different lengths, it is a scalene triangle.

Therefore, the correct answer is 2) scalene.

To determine the type of triangle RST, we can look at the lengths of its sides.

First, let's find the lengths of all three sides of triangle RST:

- Side RS: Distance between points R(3, 2) and S(-2, 3)
d(RS) = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(-2 - 3)^2 + (3 - 2)^2]
= √[(-5)^2 + (1)^2]
= √[25 + 1]
= √26

- Side ST: Distance between points S(-2, 3) and T(-2, 1)
d(ST) = √[(-2 - (-2))^2 + (1 - 3)^2]
= √[0^2 + (-2)^2]
= √[0 + 4]
= √4
= 2

- Side RT: Distance between points R(3, 2) and T(-2, 1)
d(RT) = √[(-2 - 3)^2 + (1 - 2)^2]
= √[(-5)^2 + (-1)^2]
= √[25 + 1]
= √26

Now, let's compare the lengths of the sides:

d(RS) = √26
d(ST) = 2
d(RT) = √26

By comparing the lengths, we can see that all three sides have different lengths. Therefore, the triangle RST is a scalene triangle (choice 2), since all sides have different lengths.