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!
the slope of the line joining the points is ∆y/∆x = (-3-(-1))/(2-(-2)) = -2/4 = -1/2
So, the slope of the perpendicular line is the negative reciprocal, or +2
First find the slope of the line using the formula y2-y1/x2-x1 and coordinates (-2,-1)and(2,-3)
you will get slope = -2/4 which is equal to -1/2.Slope of a line that is perpendicular to a given line is negative reciprocal.
So slope of the line 2
Oh, I'd be happy to help! But be warned, my explanations tend to be more on the humorous side. So if you're ready for some math comedy, let's dive in!
To find the slope of a line that is perpendicular to another line, we need to determine the slope of the original line first. So let's get cracking!
Using the formula for slope (m = (y2 - y1) / (x2 - x1)), we can plug in the coordinates of the given points. For the first point (–2, –1), we'll call x1 = -2 and y1 = -1. And for the second point (2, –3), x2 = 2 and y2 = -3.
Now, let's bust out our math skills and calculate the slope of the line!
m = (-3 - (-1)) / (2 - (-2))
= (-3 + 1) / (2 + 2)
= -2 / 4
= -1/2
So, the slope of the original line is -1/2.
Now, here's where the fun begins! Since we want the slope of a line perpendicular to this, we need to flip the fraction and change the sign.
The negative sign that we already had becomes positive, and the fraction flips to become its reciprocal. So, the slope of the line perpendicular to the original one is 2/1, which is just 2.
Ta-da! So, the slope of the line that is perpendicular to the line containing the points (–2, –1) and (2, –3) is 2.
I hope that cleared things up for you, in my own quirky way!
To find the slope of a line that is perpendicular to another line, you can follow these steps:
1. Find the slope of the given line using the formula:
slope = (y2 - y1) / (x2 - x1)
For the points (–2, –1) and (2, –3), the slope of the given line is:
slope = (-3 - (-1)) / (2 - (-2)) = (-3 + 1) / (2 + 2) = -2 / 4 = -1/2
2. To find the slope of the line perpendicular to the given line, use the property that the product of the slopes of two perpendicular lines is -1.
So, the slope of the perpendicular line is the negative reciprocal of the slope of the given line.
slope_perpendicular = -1 / slope_given_line = -1 / (-1/2) = 2
Therefore, the slope of the line perpendicular to the line containing the points (–2, –1) and (2, –3) is 2.
To find the slope of a line, you can use the formula:
slope (m) = (change in y-coordinates) / (change in x-coordinates)
First, find the change in y-coordinates by subtracting the y-coordinate of one point from the y-coordinate of the other point:
Δy = (–3) - (–1) = –3 + 1 = –2
Next, find the change in x-coordinates by subtracting the x-coordinate of one point from the x-coordinate of the other point:
Δx = 2 - (–2) = 2 + 2 = 4
Now, divide the change in y-coordinates by the change in x-coordinates to calculate the slope:
m = Δy / Δx = –2 / 4 = –1/2
The slope of the line containing the points (–2, –1) and (2, –3) is –1/2.
To find the slope of a line that is perpendicular to this line, you can use the fact that perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of –1/2.
To find the negative reciprocal, flip the fraction and change its sign:
Negative reciprocal of –1/2 = 2/1 = 2
Therefore, the slope of the line that is perpendicular to the line containing the points (–2, –1) and (2, –3) is 2.