Find the slope of a line that is perpendicular to the line containing the points (–2, –1) and (2, –3).
can you tell me how to do it and show the answer
Thanks!
To find the slope of a line that is perpendicular to another line, you can use the relationship between the slopes of perpendicular lines.
First, let's find the slope of the line containing the points (–2, –1) and (2, –3) using the slope formula:
slope = (y2 - y1) / (x2 - x1)
Using the given points:
slope = (-3 - (-1)) / (2 - (-2))
= (-3 + 1) / (2 + 2)
= -2 / 4
= -1/2
Now, since the line we're looking for is perpendicular to this line, we can use the relationship between perpendicular slopes. The product of the slopes of two perpendicular lines is always -1.
So, to find the slope of the line perpendicular to the given line, we take the negative reciprocal of the slope we found:
slope of perpendicular line = -1 / (-1/2)
= -1 * (-2/1)
= 2
Therefore, the slope of the line perpendicular to the line containing the points (–2, –1) and (2, –3) is 2.
I hope this explanation helps!