Find the slope of the lines that are (a) parallel lines (b) perpendicular lines to the lines passing through the pair of points (3, 4)(2,-1)
find the slopes of lines (i) parallel to and (ii) perpendicular to the line joining (6,3),(-4,5).
To find the slope of a line passing through two points, we can use the formula:
Slope (m) = (y2 - y1) / (x2 - x1)
For the given pair of points (3, 4) and (2, -1), let's label the coordinates as:
(x1, y1) = (3, 4)
(x2, y2) = (2, -1)
(a) Parallel Lines:
Parallel lines have the same slope. So, in order to find the slope of a line parallel to the line passing through the given pair of points, we can use the formula mentioned above and find the slope of the line passing through the given points.
Slope (m) = (y2 - y1) / (x2 - x1)
= (-1 - 4) / (2 - 3)
= -5
Therefore, any line parallel to the line passing through the points (3, 4) and (2, -1) will have a slope of -5.
(b) Perpendicular Lines:
Perpendicular lines have negative reciprocal slopes. To find the slope of a line perpendicular to the line passing through the given pair of points, we need to find the negative reciprocal of the slope of the line passing through the given points.
The slope of the line passing through the given points is -5 (as found above).
Now, to find the negative reciprocal of -5, we invert the fraction and change its sign:
Negative reciprocal slope = -1 / (-5)
= 1/5
Therefore, any line perpendicular to the line passing through the points (3, 4) and (2, -1) will have a slope of 1/5.
Find the slope of the line joining your two given points (you should know how to do that)
A line parallel will have the same slope
A line perpendicular will have a slope which is the negative reciprocal of the given slope
let me know what you get
Slope is 5
Parallel is 5 or 1/5
Perpendicular is -5
your slope of the given line is correct as 5
Then a parallel line also has a slope of 5
a perpendicular line will have slope of -1/5
your statement of
"Parallel is 5 or 1/5" is illogical.
same for " perpendicular is -5" , makes no sense to me.
Perpendicular is a property, -5 is a quantity
That is like saying " funny is -5"