Line n passes through points (7, 12) and (4, 15). What is the slope of a line that is perpendicular to line n?
To find the slope of a line perpendicular to line n, we need to determine the slope of line n first.
The slope (m) of a line passing through two points (x₁, y₁) and (x₂, y₂) can be calculated using the following formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the given points (7, 12) and (4, 15), we can substitute their coordinates into the formula:
m = (15 - 12) / (4 - 7)
m = 3 / -3
m = -1
So, the slope of line n is -1.
Since lines that are perpendicular to each other have slopes that are negative reciprocals, we need to find the negative reciprocal of -1 to get the slope of the line perpendicular to line n.
Negative reciprocal of -1 = -1/(-1) = 1
Therefore, the slope of a line that is perpendicular to line n is 1.
To find the slope of a line perpendicular to line n, we need to first find the slope of line n.
The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
Given that the two points on line n are (7, 12) and (4, 15), we can substitute the values into the formula:
slope of line n = (15 - 12) / (4 - 7)
= 3 / (-3)
= -1
The slope of line n is -1.
Now, the slope of a line perpendicular to another line is the negative reciprocal of the slope of that line. In other words, if the slope of line n is "m", then the slope of a line perpendicular to line n is -1/m.
Therefore, the slope of a line perpendicular to line n is -1/(-1), which simplifies to 1.
So, the slope of a line that is perpendicular to line n is 1.
m = change in y/change in x
m = (12-15)/(7-4) = -3/3= -1
Perpendicular lines have slopes that multiply to -1.
If slope = 1/2 perpendicular = -2
In this case -1 perpendicular is 1.
slope of original = (15-12)/(4-7)
= 3/-3 = -1
slope of perpendicular = -1/-1 = 1