Final answer:
To determine if the given lines are perpendicular, we need to find their slopes and check if their product is -1.
Step-by-step explanation:
To determine if the line containing points P₁(-2,5) and P₂(7,8) is perpendicular to the line containing points Q₁(-2,3) and Q₂(-9,0), we need to find the slopes of both lines.
The slope of the line passing through Q₁ and Q₂ can be found using the formula: m = (y₂ - y₁)/(x₂ - x₁) = (0 - 3)/(-9 - (-2)) = -3/(-7) = 3/7.
The slope of the line passing through P₁ and P₂ is (8 - 5)/(7 - (-2)) = 3/9 = 1/3.
Since the product of the slopes is (-3/7) * (1/3) = -1, which is the negative reciprocal of 1, the lines are perpendicular to each other.