Line "a" passes through points with coordinates (-3,5) and (0,0) and a line "b" passes through points with coordinates (3,5) and (0,0). Explain how you would determine whether lines a and b are parallel perpendicular or neither
They are not parallel because they do not have the same slope. They are not perpendicular because their slopes and not opposite reciprocals of each other. So... they are neither.
The slope for line A is -5/3 and the slope for line B is 5/3
To determine whether lines a and b are parallel, perpendicular, or neither, we can calculate the slopes of the lines and compare them.
The slope of a line passing through two points can be found using the formula:
slope (m) = (y2 - y1) / (x2 - x1)
Let's calculate the slopes for lines a and b:
For line a:
Coordinates: (-3, 5) and (0, 0)
Slope (ma) = (0 - 5) / (0 - (-3))
= -5 / 3
For line b:
Coordinates: (3, 5) and (0, 0)
Slope (mb) = (0 - 5) / (0 - 3)
= -5 / -3
= 5 / 3
Now, we compare the slopes:
If the slopes are equal, the lines are parallel.
If the slopes are negative reciprocals (opposite sign and reciprocal value), the lines are perpendicular.
If neither of the conditions is met, the lines are neither parallel nor perpendicular.
Comparing the slopes of line a (-5/3) and line b (5/3), we can see that they are negative reciprocals of each other. Therefore, lines a and b are perpendicular to each other.
To determine whether lines "a" and "b" are parallel, perpendicular, or neither, we can compare the slopes of the two lines.
1. Find the slope of line "a":
- The slope (m) of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
- Using the given coordinates (-3, 5) and (0, 0), we can plug in the values into the formula:
m1 = (0 - 5) / (0 - (-3))
= -5 / 3
2. Find the slope of line "b":
- Using the given coordinates (3, 5) and (0, 0), we can calculate the slope using the same formula:
m2 = (0 - 5) / (0 - 3)
= -5 / -3
= 5 / 3
3. Compare the slopes:
- If the slopes of two lines are equal, the lines are parallel.
- If the slopes are negative reciprocals of each other, the lines are perpendicular.
- If the slopes do not meet either of the above conditions, the lines are neither parallel nor perpendicular.
Comparing the slopes of line "a" and line "b":
- m1 = -5 / 3
- m2 = 5 / 3
Since the slopes are negative reciprocals of each other, m1 = -1 / m2, lines "a" and "b" are perpendicular.