Line a passes through points (9, 7) and (1, 2). Line b passes through points (1, 5) and (10, 10). Are line a and line b parallel or perpendicular?
To determine if two lines are parallel or perpendicular, we need to compare the slopes of the lines.
The slope of a line passing through points (x₁, y₁) and (x₂, y₂) is given by the formula:
slope = (y₂ - y₁) / (x₂ - x₁)
For line a:
x₁ = 9, y₁ = 7, x₂ = 1, y₂ = 2
slope_a = (2 - 7) / (1 - 9)
slope_a = (-5) / (-8)
slope_a = 5/8
For line b:
x₁ = 1, y₁ = 5, x₂ = 10, y₂ = 10
slope_b = (10 - 5) / (10 - 1)
slope_b = 5 / 9
Since slope_a = 5/8 and slope_b = 5/9, the slopes of the lines are not equal. Therefore, line a and line b are not parallel.
To determine if the lines are perpendicular, we can check if the product of their slopes is -1.
slope_a * slope_b = (5/8) * (5/9)
slope_a * slope_b = 25/72
Since the product is not -1, line a and line b are not perpendicular either.
Therefore, line a and line b are neither parallel nor perpendicular.