Final answer:
The points q (-1,-8), r (-8,-9), and s (-9,-2) form a triangle. To determine if these points form a triangle, we can use the distance formula. The distances between the points are not equal, so they do form a triangle.
Step-by-step explanation:
The points q (-1,-8), r (-8,-9), and s (-9,-2) form a triangle. To determine if these points form a triangle, we can use the distance formula. The distance between two points (x1, y1) and (x2, y2) is given by the formula: distance = sqrt((x2-x1)^2 + (y2-y1)^2). Let's calculate the distance between q and r, r and s, and s and q.
Distance between q and r: sqrt((-8-(-1))^2 + (-9-(-8))^2) = sqrt(49 + 1) = sqrt(50)
Distance between r and s: sqrt((-9-(-8))^2 + (-2-(-9))^2) = sqrt(1 + 49) = sqrt(50)
Distance between s and q: sqrt((-9-(-1))^2 + (-2-(-8))^2) = sqrt(64 + 36) = sqrt(100) = 10
Since the distances between all pairs of points are not equal, the points q, r, and s do not form an equilateral triangle. Therefore, the points q (-1,-8), r (-8,-9), and s (-9,-2) do form a triangle.