Line m passes through points (4, 9) and (2, 2). Line n passes through points (2, 2) and (6, 7). Are line m and line n parallel or perpendicular?
find the slopes of the lines
parallel lines have the same slope
perpendicular lines have slopes that multiply to -1
To determine whether line m and line n are parallel or perpendicular, we can analyze the slopes of the lines.
The slope of a line can be determined using the formula:
slope = (y2 - y1) / (x2 - x1)
For line m, using the points (4, 9) and (2, 2), we can calculate the slope:
slope_m = (2 - 9) / (2 - 4)
= -7 / -2
= 7/2
For line n, using the points (2, 2) and (6, 7), we can calculate the slope:
slope_n = (7 - 2) / (6 - 2)
= 5 / 4
Now, to determine if the lines are parallel or perpendicular, we compare the slopes.
If the slopes are equal, the lines are parallel.
If the product of the slopes is -1, the lines are perpendicular.
Let's check:
slope_m = 7/2
slope_n = 5/4
Since the slopes are not equal and their product is not -1, we can conclude that Line m and Line n are neither parallel nor perpendicular.