Final answer:
Triangle STU is a right-angled scalene triangle, with a right angle at vertex T and sides of different lengths determined by the coordinates of its vertices.
Step-by-step explanation:
To classify triangle STU, we can observe the coordinates of the vertices provided: S(-30, -3), T(0, -3), and U(0, 0). By looking at the coordinates, we see that points S and T have the same y-coordinate, which means that ST is a horizontal line segment. Similarly, points T and U have the same x-coordinate, indicating that TU is a vertical line segment. Therefore, it can be inferred that STU is a right triangle because it has a right angle at vertex T.
Additionally, since line segment ST is parallel to the x-axis and TU is parallel to the y-axis, we can determine the lengths of these sides by subtracting their coordinates: ST = 0 - (-30) = 30 units and TU = 0 - (-3) = 3 units. With one side being much longer than the other, we can further classify triangle STU as a right-angled scalene triangle because all sides have different lengths.
Triangle STU can be classified based on the lengths of its sides.
In this case, we can use the distance formula to find the lengths of each side:
ST = sqrt((0 - (-30))^2 + (-3 - (-3))^2) = sqrt(900 + 0) = sqrt(900) = 30
TU = sqrt((0 - 0)^2 + (-3 - 0)^2) = sqrt(0 + 9) = sqrt(9) = 3
SU = sqrt((0 - (-30))^2 + (-3 - 0)^2) = sqrt(900 + 9) = sqrt(909)
Since all three sides of triangle STU have different lengths, we can classify it as a Scalene triangle.