Answer:
Lines a and b are perpendicular
Explanation:
- In order to determine whether the lines passing through the pairs of points are parallel, perpendicular, or neither, we'll first need to know the slopes of the two lines.
- We can find the slope (m) of a line given two points on the line using the slope formula, which is given by:
m = (y2 - y1) / (x2 - x1), where
- (x1, y1) is one point on the line,
- and (x2, y2) is another point on the line.
Slope of line a:
To find the slope of line a, we can plug in (6, 2) for (x1, y1) and (9, 3) for (x2, y2):
m = (3 - 2) / (9 - 6)
m = 1/3
Thus, the slope of line a is 1/3.
Slope of line b:
To find the slope of line b, we can plug in (1, 11) for (x1, y1) and (3, 5) for (x2, y2):
m = (5 - 11) / (3 - 1)
m = -6 / 2
m = -3
Thus, the slope of line b is -3.
Determining whether the lines are perpendicular:
The slopes of perpendicular lines are negative reciprocals of each other, as show by the following formula:
m2 = -1 / m1, where
- m2 is the slope of one line,
- and m1 is the slope of the other line.
If we allow 1/3 to be m1, we see that -1 / (1/3) = -1 * 3 = -3
Thus, lines a and b are perpendicular.