Line t passes through points (8, 6) and (5, 11). Line u passes through points (9, 6) and (4, 3). Are line t and line u parallel or perpendicular?
To determine if two lines are parallel or perpendicular, we need to find the slope of each line. The slope of a line passing through the points (x₁, y₁) and (x₂, y₂) can be calculated using the formula:
slope = (y₂ - y₁) / (x₂ - x₁)
For line t passing through points (8, 6) and (5, 11), the slope is:
slope_t = (11 - 6) / (5 - 8)
slope_t = 5 / -3
slope_t = -5/3
For line u passing through points (9, 6) and (4, 3), the slope is:
slope_u = (3 - 6) / (4 - 9)
slope_u = -3 / -5
slope_u = 3/5
If two lines are parallel, their slopes will be equal. If two lines are perpendicular, the product of their slopes will be -1.
Let's compare the slopes to determine if line t and line u are parallel or perpendicular:
-5/3 ≠ 3/5
Since the slopes are not equal, line t and line u are not parallel.
Also, the product of the slopes is not -1:
(-5/3)·(3/5) = -15/15 ≠ -1
Thus, line t and line u are not perpendicular either.
Therefore, line t and line u are neither parallel nor perpendicular.